Happiness is a measure of how much the people are behind you when it comes to colonizing other planets. Without this backing your people simply aren't motivated enough to explore outside their known world. There is no cap to the amount of happiness you can accumulate on each planet, and each planets happiness is independent from the others.
Managing your waste is an important element of the game. If you don't manage it properly, you'll get pollution, which will subtract from your happiness. This article is about how pollution works, and how to manage it.
Waste is the excess produced with any kind of production. Used wisely it can be a valuable resource that can be turned into other needed resources. Used poorly it can turn into pollution that will decrease your empire's happiness. Without happiness you will be unable to colonize other planets.
Waste Chains allow you to automate the removal of waste from your colony and dump it into your local star.