I see now, and yes I wondered if that was what PlutonianEmpire meant. That is certainly one of the most discussed methods of starting the process of terraforming Mars. There are also many other proposals about how to make it breathable for humans using various methods, all only limited by money, imagination and the desire to do it. I hope this answers your question properly.
Current conditions in the Martian atmosphere at less than 1 kPa of atmospheric pressure, are significantly below the Armstrong limit of 6 kPa where very low pressure causes exposed bodily liquids such as saliva, tears, and the liquids wetting the alveoli within the lungs to boil away. Without a pressure suit, no amount of breathable oxygen delivered by any means will sustain life for more than a few minutes.
There are 3 key steps into terraforming Mars that must work and need to last if we want to walk around a talk and stuff.
#1) Building up the magnetosphere:
From about 1500 nanotesla up to around 65000 nanotesla. You could also simply ignore that and realize any atmosphere you do add would slowly be blown away by the solar winds, but it would be a VERY slow loss. By then we might have the ability to mitigate the moderate atmosphere loss from solar wind in other ways.
Nukes have been suggested to be dropped in holes drilled all the way through the crust in hopes of melting the core and restart an internal dynamo of molten iron thereby creating a large enough magnetic field, planet wide. Another misuse of nuclear power is Elon Musk's desire to nuke the poles to speed up the pace of terraforming but I think it would serve a better purpose to propel rockets to Saturn and collect water from the icy rings. Or you could simply crash one of Jupiter's moon into Mars.
Another point is the northern hemisphere of Mars is much less magnetic than the southern hemisphere. If Mars at one point in the past had an internal dynamo like Earth's, rocks that formed on Mars before the dynamo shut down will remain magnetized. Any rocks that formed after the dynamo shut down, or that were heated above their Curie point (the temperature at which their magnetic domains randomize, which differs from mineral to mineral, but which is in the ballpark of a few hundred degrees Celsius) after the dynamo shut down, will not be magnetized.
Perhaps a glancing blow from a truly gigantic impact stripped away most of the northern hemisphere's crust, and since nothing is perfectly spherical, temperature differences in the crust allowed the dynamo to continue but only affecting the thicker crust areas in the south. That shows Mars could indeed lose it's atmosphere to solar wind while still having an active core and magnetic field on one half of the planet.
My favorite way would be to build a giant planet-encircling electromagnet. First, string a protective pipeline all the way around the planet; around the equator is good, but any great circle path will do, so pick whichever your surveyors and civil engineers say is most convenient, then fill the pipe with a continuous loop of superconductor cable with a correct number of windings to meet whatever magnetosphere standards you have. You will need to do this multiple times to get a high enough value of current.
Build solar panels on top of the pipeline to provide power. Once it's charged up, the superconducting coils won't require a power source to keep going (since they are, after all, made of superconductor), but you need a way to get them going in the first place, and after wards the solar panels can be used to power other things like lights and equipment for the convenience of maintenance workers.
#2) Building up the atmosphere:
Mars's CO2 atmosphere has about 1% the pressure of the Earth's at sea level and currently has a mass of 2.5 × 10^13 kilograms. This is about 1% the mass of Mt Everest. The planet Mars itself has a mass of about 11% of the Earth. If we could raise the mass of the planet it would naturally increase the mass of the atmosphere. However, we would need to find 8 additional Mars sized objects floating around nearby and crash them into Mars, plus adding mass to a nearby planet is a little tricky.
Disturbing the current orbital resonance from adding that much mass to Mars could kick Earth into the sun. One solution is you could divert some of the denser asteroids from the asteroid belt nearby and calculate their momentum such that there is no net gain in the orbital velocity of Mars when they impact its surface, sort of "driving" it along with asteroid impacts as it builds mass. I'm pretty sure this would turn the surface of Mars into a boiling sea of melted rock though and humans are not patient enough to let a cake cool down out of the oven.
Since the mass of the planet is probably harder to change than the mass of the atmosphere, we'd need to increase the mass of the atmosphere by about 200 times in order to even get close to the air pressure in the Himalayas, which as you know is way less than sea-level. So good luck getting 2 Mt Everest's worth of gas onto Mars.
It is estimated that there is sufficient CO2 ice in the regolith and the south polar cap to form a 30 to 60 kPa atmosphere if it is released by planetary warming. The reappearance of liquid water on the Martian surface would add to the warming effects and atmospheric density, but the lower gravity of Mars requires 2.6 times Earth's column air mass to obtain the optimum 100 kPa pressure at the surface. Additional volatile gases to increase the atmosphere's density must be supplied from an external source, such as redirecting several massive asteroids containing ammonia (NH3) as a source of nitrogen.
If Mars atmospheric pressure could rise above 19 kPa then a pressure suit would not be required. Visitors would only need to wear a mask that supplied 100% oxygen under positive pressure. A further increase to 24 kPa of atmospheric pressure would allow a simple mask supplying pure oxygen. This might look similar to mountain climbers who venture into pressures below 37 kPa, also called the death zone where an insufficient amount of bottled oxygen has often resulted in hypoxia with fatalities
We still need that 20% of O2 you spoke about. So next, set up solar panels that will use the energy they generate to break the Martian CO2 atmosphere into carbon and oxygen. But CO2 is really stable and carbon needs something to bond with, so where are you going to come up with a material to serve as your carbon sink? Plants, and Algae take care of the carbon levels. Drive a few ice chunks from Saturn's rings into an area to create freshwater oceans. The water will evaporate and help thicken the atmosphere. We all know how important Water Vapor is, right? At this point Water Vapor in the air would be close to that on Earth, so no need to worry about desiccation or pushing aside Oxygen in your lungs because temperature and air pressure would be normal. Now the additional 20% O2 you requested is in the Martian air!
#3) Raising the temperature:
This is easily accomplished by importing 40 million metric tons of ammonia or hydrocarbons. A personal favorite is using Sulfur Hexafluoride, excellent because it is non-toxic & inert and 6 times heavier than oxygen. What's really cool is it makes your voice sound like a vocalist for a Death Metal band, kinda the reverse of what helium does. It too can be mined from the mantel of Mars. Bringing in large amounts of ammonia from comets will serve as additional greenhouse gases to melt the polar ice caps, again pumping up the weight of the air.
Reducing the albedo of the Martian surface would also make more efficient use of incoming sunlight. This could be done by spreading dark dust from Mars's moons, Phobos and Deimos, which are among the blackest bodies in the Solar System and they are already on a collision course with the surface in a million years or so; or by introducing dark extremophile microbial life forms such as lichens, algae and bacteria. The ground would then absorb more sunlight, warming the atmosphere.
So now we have the right gases, the right pressure and the right temperature!
Lets set up camp and name it PlutonianEmpire!
Hopefully I can smoke this cigarette on Mars without it burning up like a primer cord!