The attack move is simply that. It is an attack order issued to your units, should any peaceful attempts fail. It is mainly used to resolve all conflicts, much like how real wars are. Most units are set on auto attack which causes them to destroy anything they encounter that they can, their range can be customized in the tactics management menu. Certain ships such as colony or scout frigates are not on auto attack so as to prevent them from trying to take on something that can destroy them in one volley. This can be used to your advantage against an AI, as they will often leave colony ships to be destroyed if you attack a new planet of theirs.