Hi Grace,

Core aeration of the lawn can help mitigate compaction, thatch, and bumpy lawns.  It's recommended for high traffic lawns and lawns in new areas, which usually face compaction issues.  In order to be effective, though, the holes have to be quite close together--on 3" centers.  This is certainly more than one pass with the machine.

Depending on the traffic level of the lawn and its condition, aeration can be done once, twice, or multiple times in the growing season.  Spring and fall are both acceptable times.

Low traffic lawns or established lawns that are doing well probably do not need to be aerated, at least not annually, but doing so will not hurt them.  

Usually the plugs are left on the lawn.  For managing thatch and bumps, the plugs should certainly be left on the lawn; otherwise you can remove them if you prefer. 

More information on aeration and all lawn care can be found here:https://extension.colostate.edu/topic-areas/yard-garden/lawn-care-7-202/

I hope this is helpful!

Cordially,

John