Alkylation is a term in organic chemistry which means to form a carbon-carbon bond (simplifying, but accurate enough). This is actually somewhat difficult to do - it turns out that carbons are actually quite stable. For context, organic chemistry tends to work with a carbon "core" that doesn't really change a ton, with a bunch of random other atoms stuck on the carbon core. And you typically mess with the other random atoms rather than the carbon core.

However, in some semi-specific cases, you can manipulate a molecule to be unstable enough that it would be willing to break or form carbon bonds. Many forms of alkylation involve using a second molecule that contains a carbon bonded to a bromine or iodine (in this case, the molecule is C2H5Br). The end result is that your molecule (the one you want to modify) kicks out the other molecule's bromine, and a new carbon-carbon bond is formed in its place. Basically, you've just fused the two molecules together.

The meme is just showing several examples of C2H5Br being used as the "secondary molecule" and being fused onto things that make zero sense.

Edit: ironically, the last example ("alkylating agent itself"), despite sounding the most absurd, is actually probably the most feasible example to alkylate