Fleets are the core of your forces in the game. They take over new systems, discover galaxies, examine Curiosities, fight with enemies. Each ship has a certain amount of Command Points. The bigger the ship, the more Command Points it requires. Each fleet in your empire can consist of a certain amount of ships which is based on the total amount of Command Points. Almost every faction starts the game with 4 Command Points per fleet. This number can be increased by developing new technologies. It is very important because the biggest ships require 6 Command Points. The more ships you have in a fleet, the more firepower you have. Only one fleet can participate in a battle. If you have 20 ships in total but they are divided into fleets with 4 ships per fleet and your enemy has only one fleet with 10 ships (or the total amount of Command Points is 10) then the enemy's chances are greater and they can destroy your fleets without any loses. Remember that your fleets heal and resupply their crews faster when they are in your systems.
Hangars are places that store your ships on planets. They can keep an unlimited amount of ships, however those vessels don't participate in battles and can't support defense systems. On the other hand, when enemy's fleet is bigger it is wise to wait with producing additional ships and send one of your stronger fleets. If your fleet is orbiting your system you can move your units on a planet.