In the simplest terms, the noun medium is a go-between.
In art, it's a material used to create, like oil paint or clay. In science, it's a substance through which something is transmitted, like air. In communications, it's a means of sharing information, like the Internet or TV. Medium can even refer to people who purportedly communicate with the dead; they're a go-between connecting the living and the spirit worlds.
The word medium has two plural forms—mediums and media—and which one you use depends on what you're talking about.
If your subject is art, it's okay to use mediums or media. For science and communication, media is generally preferred. And if you're talking about fortunetellers and psychics, you always refer to them as mediums.
(Aren't you glad we started with the simple version?)
"Facebook used to be my favorite social medium. Then my mom signed up."
Moms: inescapable since the beginning of time. Since this sentence is talking about just one means of sharing information, Facebook, medium is the correct word.
"The disgraced mayoral candidate tried to blame his political downfall on the media, but the voters knew it was really because of the scandalous affair he carried on for close to ten years."
In this all-too-familiar example, media is the correct word because it refers to the mass communication industry that covers TV, the Internet, newspapers, journalism, and so on.
"My two-year-old nephew is an amazing artist. His favorite mediums are crayon and spaghetti sauce."
Sounds like the speaker has a pint-sized Picasso on his or her hands. When you're talking about art, it's generally acceptable to use either mediums or media as the plural form of medium.