Methane is the simplest Carbon molecule, with one carbon attached to four hydrogens. It is a light molecule so in ordinary circumstances, it is a gas. It is colorless and odorless. While today we know of “cow farts” and the effect of methane on global warming (damages the ozone layer), back in the day it was a killer of miners. It would accumulate in mines, pushing out oxygen but sometimes not discovered until it was too later. Hence the term “canary in the coal mine”, where canaries, sensitive to methane, were used to detect methane before the miners entered.
A “Methyl Group” is a methane molecule that is missing one hydrogen, which allows it to attach to other molecules (see diagram on the left). Often methyl groups are linked up in a “carbon chain”. In other cases they can form more complex branching shapes. For example, most enyzymes are complex carbon structures that contain metals such as zinc, selenium or iron, harnessing and containing their power, like the cement, steel and water surrounding the plutonium in a nuclear power generator.
Methylation is the attachment of a methyl group to another molecule. It is often used to turn genes and enzymes on and off like a switch. You can look at your genes as a library or database of information about which switches should be turned on and off. Since genes can indeed be turned on and off, your genetics only determine 20% of your health, the other 80% is lifestyle factors that turn your genes on and off in patterns that we call health or disease.