The other name for the symbol is a Lemniscate which comes from the Latin word meaning decorated with ribbons. It was first used to denote mathematical infinity in 1655 by mathematician John Wallis. Since Wallis first used it the symbol has been used to represent a number of different concepts such as hope, eternity and empowerment.
The infinity symbol is a popular choice for gifts because it symbolizes everlasting love, loyalty and a lifelong friendship. It also is thought by some to represent faith and one's relationship to God.