Paratroopers don't have the heavy weapons they need to take ground or to some extent even hold it. So, when they are deployed the mission has to fit within those limitations.

That usually translates into securing a position against minimal resistance and then reinforcing them as quickly as possible. The example of an airfield is a good one. Another could be a lightly defended port or naval landing site.

They could also be used to destroy bridges and others critical infrastructure when you need something bigger than a "special forces" unit, but then a means to evacuate them has to be put into the mission or link up with them has to be put into the plan.

Airborne forces are expensive to train and so only make sense in a very large army that can afford to dedicate a small portion of its force to train for these very specific missions.