The name Metamage is a salute to Douglas R. Hofstader’s Metamagical Themas, a column which appeared in Scientific American (and was subsequently published as a book), and which in turn is a salute to (and anagram of) its predecessor, Martin Gardner’s Mathematical Games column.
The prefix 'meta-' means that something pertains to itself: For example, a wish concerning wishes (e.g. "I wish that my previous wish be canceled") is a meta-wish. Metamagic, then, is the use of magic to augment, resist, control, or otherwise affect other magic. If elemental magic enables you to shoot lightning bolts from your fingertips, metamagic permits you, say, to create a wand that allows someone of lesser skill to cast lightning bolts.
A mage is one who uses magic — a wizard, perhaps. A metamage is one who practices metamagic. Analogous to the metamage is a software developer who writes development tools.