A useful feature on DSLR cameras is the button (or buttons) designated to lock the exposure, or lock the focal point.
Refer to your user manual for the method/button of controlling these features as they vary extensively with camera models. Canon (pictued left) may use a button labeled with an asterisk (*) but on some models that button can be set through customized settings to control Either AF-Lock or AE-Lock. Nikon often has a dedicated toggle button.
The purpose of Auto-Exposure Lock (AE-L) is to enable you to capture the desired light metering from one portion of the image, then re-frame the image without losing the exposure.
Consider the images below. In the left image, the sky is too bright for the quality of photo sought by the user. The middle image is too dark, and the right image is the preferred outcome. In the left image, the user likely caught metering of the dark foreground, which told the camera there was not enough light for the whole image; resulting in a sky that was over-exposed by the camera thinking it needed more light for the exposure. In the middle image, light was metered from the lighter background, resulting in an under-exposed foreground (plant and floor).
In these situations, the user frames the image to capture the best light metering (often with a little trial & error), presses the AE-LOCK button to hold the exposure for a few seconds, re-frames the image to capture the desired scene, then takes the exposure with the shutter.