In its most basic description, editing is the name given to the act of taking a bunch of individual shots, and deciding which order to put them, and where each shot will start and end.
To do this effectively, you need to be working in a medium where you can quickly make changes and review those changes in realtime without having to render every time. Editing is where you set the pace of your film by carefully deciding what you show the viewer and when.
Great rushes can be ruined by a poor editor, but a great editor can often make poor rushes look good!
Editing packages are designed for the specific purpose of letting you pick and choose your shots, make the cuts, make changes, review your choices, make multiple versions to compare.
After Effects, on the other hand, is designed to let you bring your chosen shots and create special effects using those shots, then render them out so they can be added to your edit timeline.
Its flexibility lies in its ability to let you design and composite effects from multiple layers, using many different plug-ins.
Yes, you can edit in AE but its not designed for that, and so you have to compromise. Every cut will need to be rendered to watch it back. You won't be able to watch all your film in realtime.
Just like in most editing software you can do some effects - but they are a compromise, so the effects are never particular good.