The Galadhrim were the inhabitants of Lothlorien, the wood ruled by Galdriel and her husband Celeborn.
The Galadhrim were Sindar elves, meaning that though they had seen Valinor, they did not posses the same unearthly power of their Noldorin brethren. In elf kingdom in Mirkwood, Sindar were childlike, taunting, and playful. But their kindred, the Galadhrim, were more wise and serene.
The Galadhrim were exceptional archers, having honed this skill over many centuries. Perhaps most notable was Haldir, who caught the fellowship (including Legolas) entirely unawares, bow drawn and ready to shoot.
The Galadhrim defended their home against orcs, who attacked around the end of the Third Age, just before Sauron was destroyed. The Galadhrim weathered all of the attacks. For a more complete history of these battles, see Lothlorien.