Cross sectional study is when you take a snapshot at the population at a moment in time.
It's observational, you observe what's there in that subset of the population at that particular time.
It's usually used to calculate prevalence.
For example, you want to know how many influenza patients you have in the hospital during the month of December. That's a cross sectional study. You can't calculate incidence from it.
You can assess some parameters from the cross sectional study, like for example you see what percent of your influenza patients did not take flu shot, this is used to assess relative risk but if you want to measure the absolute risk you need to do case-control and follow them in time.
If you follow your influenza patients in time and see what happened with them, then your study is now converted to a longitudinal study and it's not cross sectional anymore.
Note that following them in time, is not necessarily forward, it can be backward, like for example checking their previous health history and see why they got sick. In that case the study will be called retrospective study and won't be called cross-sectional anymore.