Circles around ships

[Gilead Abyss]

I'll give the short answer, and others here will certainly expand.
The full and partial circles around surface vessels represent the approximate detection ranges: visual and sonar. This is affected by several factors in the vanilla game, and some of the mods change this further.

If you are just getting started, look through the "Skipper's bag of tricks" sticky at the top of this page for introduction and training, and search this forum or post questions as them come up.