A methyl group is the name given to single carbon (with 3 hydrogens attached) when substituted onto a larger chemical moiety (a structure or motif in chemistry). When people speak about methyl groups they’re mostly speaking about those single carbon methyl group being attached to a heteroatom (atoms other than carbon and hydrogen in organic chemistry, like nitrogen, oxygen, sulfur, etc.).

Methamphetamine (N-methylamphetamine or N-methyl alpha-methyl-phenyl-ethylamine in full form) has a methyl group on it’s amine (nitrogen or N-position), which drastically alters its psychological effects and the way it’s synthesized by chemists (requiring methylamine). The methyl group there prolonges the stimulating effects, while also providing serotonergic effects (generally euphoric effects caused by interaction with the serotonin receptor transport protein), which gives it much greater addiction potential.

Methyl groups in general don’t “make drugs stronger” like the other guy said. To consider drug receptor interaction you need to take into account how well a molecule fits into the receptor you’re targetting as a whole.