They represent the D&D standard-elves rules-wise.
They have all the characteristics of elves as described in the PHB, with the exception of height and weight, but all elves on Faerûn are as tall as humans, and have more weight than elves in standard-D&D (except dark elves). They the most numerous sub-race, and the most tolerant to other races.
They're usually nomadic, becoming restless if they're at the same place for more than one or two years. Their skin is usually white, often tinged with blue at places, and their hair is often black or very dark blue. They are called moon elves or silver elves.
Sometimes they're called gray elves (not to confuse with the standard-D&D gray elves - in the Realms, the sun or gold elves are the arrogant bastards). If it's a human or member of another race, it usually shows that the name-caller's ignorant of elven culture. Uttered by another elf (most of the time, it's uttered by gold elves), it becomes a mortal insult. If you change the elven pronounciation of the word just a bit, it becomes dross - the by-product you get when you work with gold (the analogy obvious).
Moon elves are just one of several elven subraces on Toril. The complete list includes Avariel (Winged Elves), Moon (or Silver) Elves, Sun (or Gold) Elves, Wood (or Copper) Elves, Wild (or Green) Elves, Aquarian (or Sea) Elves, and Drow (or Dark Elves). In the Yuirwood of Aglarond, there are also Star (or Mithral Elves), and there's a special kind of Tiefling that's a crossbreed of Gold Elves and Demons (usually Succubi/Incubi), called Fey'ri, but that one's very rare, numbering less then 100 individuals, all belonging to the same clan.