What are the effects of the approval rate?

It affects your race's "friskiness". Low approval = lower birthrate.

Ah ok, I see. So by lowering your taxe rate you increase birth. I have another question: does a morale building (entertainment etc..) has an effect only on the planet it is built or does it have an overall effect on your empire population?

There's a decent article at the galwiki on Approval.

Two effects I try to keep a close eye on are: 1) population growth and 2) Senate votes within my empire.

For me, high approval is most important in the long middle of a game (I typically play gigantic maps with common/abundant real estate). In the early game, I have too much to do to worry about max pop growth, but once I have several colonies going I *really* start needing income, which means I need peeps. In the late game, when most of my planets are fully developed, I still try to keep ratings green but don't worry as much about getting the max pop bonuses.

If you never switch your gov't from dictatorship, point 2 is moot for you. But having your party lose the Senate is a real drag, regardless of which party you like to play.

does it have other effects?

Yes. It affects the vote in the Senate. If your approval drops too low, and you lose an election, you will lose any bonuses that your party affiliation gives you.

It affects your race's "friskiness". Low approval = lower birthrate.

Don't confuse approval with morale. Morale on an individual planet will affect the birthrate for that planet.

by lowering your taxe rate you increase birth.

Yes, it can do so. Lowering taxes raises morale, which, again, affects birthrate.

does a morale building (entertainment etc..) has an effect only on the planet it is built or does it have an overall effect on your empire population?

It only affects the planet on which it has been built. Mining a morale resource will affect your entire empire. If you would like to see the exact numbers, take GW's advice and visit the Wiki.