Time slows down with speed compared to what reference point? So as far as I understand time dilation it means that time slows down as an object approaches lightspeed. This is an issue even with for example satellites around earth compared to people on earth (GPS).
Now I am wondering compared to what reference point is this speed measured? Is it absolute speed in comparison to the spacefabric (is that even possible to measure?)?
If thats true then how come that the speed of the satelites around earth has an impact at all? I'd imagine it to be similar to me running back and forth on a plane. In the end my average speed will be the same (If I sit back down on my place) compared to me sitting down the whole time. Does that mean, that time dilation was the same?
 A: 
Now I am wondering compared to what reference point is this speed measured?

The reference “point” is a system of clocks, all of which are at rest in the chosen reference frame and synchronized. The time on the moving clock is compared to the time on the co-located stationary clock at each moment, and the time dilation is calculated from that.

I'd imagine it to be similar to me running back and forth on a plane. In the end my average speed will be the same (If I sit back down on my place) compared to me sitting down the whole time. Does that mean, that time dilation was the same?

This is a version of the twins paradox. The back and forth time dilation does not generally cancel out.
A: You will get confused if you think that in Special Relativity time slows down in some absolute sense- it doesn't. In SR all motion is relative, and time dilation is relative. So, when you talk about an object moving at close to the speed of light, you have to answer the question 'relative to what?'. As you sit in your chair reading this, you are moving at close to the speed of light relative to a passing muon and your time is dilated, so that a second of your time is like a minute in the frame of the muon. Relative to a passing spaceship traveling at 0.5c, your time will be dilated by a different amount. So the degree of dilation is not absolute- it can take virtually any value depending on which reference frame you pick to measure it from.
Remember also that time dilation is entirely reciprocal, so if the interval of a second on your watch is equivalent to an interval of a minute in the frame of the muon, then an interval of a second in the life of the muon is equal to an interval of a minute in your frame.
If you wonder how time dilation can be reciprocal in that way, the answer is that time doesn't 'slow down' in the way you might think. A second on your watch is the same duration as a second on the watch of somebody moving at close to the speed of light relative to you. What causes the effect of time dilation is that the clocks in your frame are not synchronised with the clocks in the other frame. To see this, imagine you are walking down a corridor with clocks on the wall every 10 meters, and each of the clocks is running at exactly the same speed as your watch, but each is set to be a second ahead of the previous clock. As you walk down the corridor your watch will seem to start getting further and further behind the clocks on the wall, losing another second at each clock you pass, so it will appear that your watch is running slower than the clocks, but really what is happening is that your watch is running at the same speed as each individual clock, but in the frame of the clocks, where time advances by a second every ten metres, your watch time gets more and more behind (ie it seems dilated).
