I don't really understand it better than you probably, but as far as I can tell:

Geostationary means that it remains still to a ground observer. As the earth rotates, the satellite is rotating at the same speed. So if a satellite is stationed over New York, day or night it would remain over New York. This doesnt mean it's not moving. It is like two cars driving the speed on the freeway, but with orbits instead of linear roads. They could be going 2,000 MPH but you would still be able to look over and see the other cars driver.

Retrograde means it's moving in the opposite direction. Idk which way the earth rotates, but in general satellites move in the same way (pretty sure). So to keep the road analogy: you are on the freeway and cars usually are passing you or you're passing them, going different speeds but in the same direction. But then all of a sudden a car comes flying in the opposite direction - that is a "retrograde" car.

As people have mentioned, the phrase is an oxymoron. Something cannot have the properties of remaining stationary over a point on earth (geostationary) and also be traveling in the opposite direction of our orbit (retrograde).

What they are trying to say is they want this satellite to be at the same orbit distant as other geostationary satellites (35,786 km from the equator, but want it moving in the opposite direction as all other satellites so they can check on other satellites in hours by moving in the opposite direction. Instead of having to go very fast and only be able to check on the satellites every few days,

She bought an engagement ring for herself and hoped you would take that ring and propose with it? I find that stranger than hiding it in a mattress