AE Lock is for situations where you want to use metered exposure later than you metered it:

• locking exposure capturing parts of a panorama - for seamless stitching, frames with similar exposure will work better than differently exposed ones;
• when you meter from a gray card, lock exposure, then remove the gray card and compose;
• you point your camera on a surface that should be exposed as 18% gray, lock exposure, recompose

AE Lock is for situations where you want to use metered exposure later than you metered it:

• locking exposure capturing parts of a panorama - for seamless stitching, frames with similar exposure will work better than differently exposed ones;
• when you meter from a gray card, lock exposure, then remove the gray card and compose;
• you point your camera on a surface that should be exposed as 18% gray, lock exposure, recompose
• as @mattdm commented - when there are areas that would confuse matrix metering, compose so they are excluded, lock exposure, recompose

AE Lock can be thought of as a "quick version of temporary M mode". As such, you can quickly lock metered exposure and take a few shots with it. Most cameras will unlock AE after some idle time, so manual mode is more suitable when you work slowly and want to tweak things little by little.