Premiere is a top notch NLE that works on a lot of levels with a steep learning curve. At its most basic it will allow you to capture video from a number of sources, edit it as much or as little as you want and then give you a lot of export options when done.

After Effects on the otherhand is specifically aimed at the creation of special effects, animation and motion graphic creation and isn't an NLE. You would bring it into your production pipeline after the initial edit was done of the video.

You can add effects using Premiere but it doesn't have the same amount of effects that AE has nor does it offer the same level of control over the effects. One thing that's always puzzled me is its name, After Effects, surely it should be called Before Effects (as you have to use the package to apply the effects), unless you've already used another effects package to add effects to your video.

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