The Grammy Award for Album of the Year is the most prestigious award category at the Grammys. The difference between Record of the Year and Album of the Year is that while Record of the Year is awarded for a single or for one track from an album, Album of the Year is awarded for an entire album.
So, in the context of the Grammy Awards, "record" means one song and "album" means the whole collection of songs on a CD or LP. In essence, "record" really just means single.
edit Recipients of the awards
The Record of the Year is awarded to the performing artist, the producer, recording engineer, and/or mixer for that song. Album of the Year is awarded for a whole album, and the award is presented to the artist, producer, recording engineer, and mastering engineer for that album.
edit What about Song of the Year?
One may wonder that if Record of the Year is awarded for a single song, then what about Song of the Year? The Song of the Year is also awarded for a single song but the award is for the songwriter who composed the song. Unlike the Record of the Year, which is awarded to the entire team involved in producing the song, Song of the Year is for an individual contributor - the songwriter.