Jason Boone covers and easy way to create easy backgrounds with After Effects Shape Layers.
There are a lot of features in Ae that are helpful to a lot of workflows. One of them is the shape layer workflow. Shape layers allow you to create vector artwork, but they also come with a whole host of tools under that magical “add” button under the layer’s attributes. Jason Boone shows how to use the repeater addition to create interesting backgrounds fast.
The whole system is also a great way to make patterns (be it for background or something else). Have a look at one of Evan Abram’s tutorials that explored methods for designing patterns that were infinitely seamless and also animated. Ae has a few other helpful tools for this, with effects like Motion Tile, RepeTile, and HexTile.