On the topside where you grow your plants, you will find an Oxygen Filter to the left-hand side. You will regularly need to repair this to ensure that the air quality is breathable for the people below.
However, another thing that you need to consider is how many people reside in the bunker, as the filter only has a limited supply. To keep people in the business of that good old fresh air, you will need to Upgrade the filter.
When the bunker reaches a certain amount of inhabitants, the game will start to warn you about the dangers of suffocation if there are too many people residing in the bunker. For the first upgrade, you will need Five Buckets and Five Pipes to increase the Output. This will increase the amount of air in the bunker.
You will also need to upgrade it in the Resistance and Durability categories, as well, so that it is more robust against such things as dust storms.
Need more help keeping those survivors alive? Check out how to get clean without a shower in Sheltered 2!