One of the biggest differences between Adobe After Effects and Final Cut Pro is the way in which they access the media you use in your projects.
AE uses reference paths to point to the clips you require, making it very easy to store those videos externally, but also slows down the rendering process for playback in the editor. Final Cut imports the clips to 'Libraries' which can only be read/opened from within the application itself. This makes the editor faster at rendering, but these 'Libraries' can soon become very bloated, and choke/slow down your mac overall.
This tutorial walks you through moving your Final Cut Pro Libraries to an external hard drive, and pointing Final Cut to that new location, so you can store your files externally and get back that space and speed.