Those are the edges of sensor circles, they mean that you're within the detection range of some fleet. The color indicates what fleet it is, e.g. yellow = Hegemony. If you make yourself less visible, e.g. turn your transponder of, go dark or hide in a nebula, the circles become smaller.
At the beginning usually pirates find you, just fly around until they attack. You can of course visit typical pirate locations to speed this up, like pirate stations or wormholes (hyperspace site is best). Or you follow around a patrol and fight with them.