Maiar (singular Maia) are angelic beings of great power. They were called into being by Ilúvatar before the world, Arda, existed. They aided the more powerful Valar in creating and adorning the world in preparation for the coming of Elves and Men. Notable among the Maiar are Sauron, Gandalf, Saruman, Radagast, Melian, Uinen, Ossë, and the Belryg of Morgoth.
Maiar can be a broad category, referring to most powerful spirits that don't rival the Valar in strength. Some are named as Maiar in Tolkien's works- the Wizards, Sauron, the Belryg (fire-spirit Maiar corrupted by Morgoth), Melian- but others are not so clear. Shelob is considered by some to qualify as a Maia, along with her mother Ungoliant (whatever they are, they are certainly powerful). The River-maids, extrapolated from Goldberry for the purposes of Lotro, are often considered among the Maiar as well.