Not everyone is a materials expert, so when someone asks the question "What happens when metal X touches metal Y?", you don't have to feel bad when you don't know the answer. Except when it comes to gallium and aluminium, in which case you'll sound like some sort of SCIENCE WIZZARD (feel free to put that on a hat).
Of course, you'll have to watch the video above for the explanation -- and rather fascinating visuals. It's a few years old now, but the clip from YouTube channel TAOFLEDERMAUS still does the job.
It starts with two drops of gallium on an upturned aluminium heatsink. Nothing happens for the first 30 minutes or so, but eventually the gallium is absorbed into the other metal. It then goes all T1000, making the surface almost liquid.
Finally, the heatsink becomes extraordinarily brittle, with the fins crumbling like an arrowroot biscuit.
Outside of the curiosity aspect, I can't say why you'd do this to a poor heatsink. If you do try it though, make sure to detach it from your computer first.