When you create a title or graphic in After effects, you may want to composite the render over footage in your editing application instead of AE. To do this you need to simply export your video with the alpha/transparency information.
To render it this way, add your comp tot the render queue (be sure to have no background layer) and use QuickTime as the output format. Select a codec like Animation or PNG and be sure to change the depth to RGB + Alpha. This option is not available for all codecs.
Some editing applications like Vegas video require you to set the properties of the footage to premultiplied so that it will interpret the transparency correctly.