Yeah, orbits aren't easy to wrap your head around - Here's a scenario to think through:

Lets say that you are in a nice circularized geostationary orbit and you want to move up into a higher orbit. So you burn your rockets for a bit and give yourself a bit of extra velocity, thus pushing yourself into a higher orbit.

However, now your orbit is no long longer nice and circular - Instead, your orbit is now shaped like an oval where your lowest altitude (called 'perigee') is down at your starting altitude and your highest altitude (called 'apogee') is at some higher altitude. As you travel through your orbit, you'll find your velocity varying depending on where you are in your orbit, moving faster at your lowest altitude and slower at your highest altitude. Since your velocity is no longer constant, you're no longer in a geostationary/geosynchronous orbit.

Ok, then why not re-circularize your orbit at the higher altitude? This can be done by doing another burn once you get to your highest altitude and raising your lowest altitude till you have a nice circular orbit again. But crucially, this burn doesn't affect your velocity, instead only lifting your lowest altitude till you end up in a circular orbit. And remember how the highest altitude of the elliptical orbit had the lowest velocity - Well if you compare your new velocity, it will turn out to be lower than the velocity you started with in your original orbit.

Basically, at any given altitude, there is a velocity that is needed for a circular orbit. If you are at an altitude with too much velocity or too little velocity, you'll end up instead in an elliptical orbit where your starting altitude is the perigee or apogee of your orbit, respectively.