When you first click on the map link you will come to a page with a picture that looks like a galaxy.
Whether you realise it or not this galaxy is split into different sectors, each of which can be clicked on.
The map screen shows a star map of the galaxy you reside in. The edges of the galaxy are connected, so you can directly travel with your fleets from the bottom to the top of the galaxy, without needing to cross the galaxy. This is one of the main hubs in the game, and you can perform a great variety of actions from the map.
All the stars that you see represent different solar systems. The systems which you have a presence in will have a blue circle around them. Similar, the homesystems of your allies/NAPs and enemies are marked with a green circle stating Ally (Ally/NAP) and a red circle stating Enemy.
Click on any of the systems to access it, and a pop up window will appear, where you can see the planets the system consist of.