Cloud Computing gathers all data to a central computing facility (data center) and performs computation centrally there.
It is called centralised computing, and sometimes feudal computing to insist on the fact that there is a computing lord and castle, on the other side of the Cloud, and that all data go there, as farmers-servants would have to do in the Middle Age in Western Europe.
Edge Computing keeps the data where they are acquired and does pre-processing there, before shipping the result further for other processing.
It could be compared with fishing, with freezing of the fish as soon as it is fished, on the ship.
Imagines many visual sensors. You might send raw pixel data on the Cloud, or you might encode the pixels forming an image with an MPEG codec for an efficient compression. In this second case you save orders of magnitude in transmission consumption, but you have to use energy for computing at the source point (battery powered possibly).
Depending on the application Cloud or Edge computing may be preferred or a mix of the two...