Bracketing on DSLR camera?

Can someone explain what bracketing is on a DSLR? I'm looking at getting my first one.
Also does the Canon T1i and Nikon D3100 have the bracketing feature?

Bracketing is the process of taking three photographs of the same subject; one at the proper exposure, one at one stop above and another at one stop below proper exposure. This is to ensure that at least one of the photos comes out with the correct exposure even if you're a little off on your settings.
Most Digital SLRs can be set to do this automatically instead of you have to adjust the settings for each of the three photos like we had to do in the old days of using film cameras.

It is so simple to bracket exposures, it is not the best reason for picking one camera over another.
Better see which of those two cameras can use auto-focus in the video mode. That might be a better criteria for choosing a camera

Sounds like you are wanting to shoot HDR images perhaps? All dSLR cameras should be able to do AEB (auto exposure bracketing). But check the specs or manual first. The T1i definitely does.
When using AEB (for HDR) set it, then turn the mode dial to Av (aperture priority) to maintain your depth of field and shoot keeping your finger down on the shutter button till the camera takes three shots (one correctly exposed, one over, one under).
If you can afford it, I recommend the T2i instead…