As with most tattoos, the meaning is usually personal to the individual who got the tattoo. That said, the most common meaning of infinity tattoos is to reflect eternity in some way.
The infinity tattoo is popular with couples because it is a safe tattoo to represent their unending love. Couples usually get the tattoo in the same spot on their bodies, and usually have hearts accompany it. But, people can use the infinity symbol for anything that makes sense to them. The pseudo-religious connotation is that it symbolizes humans are eternal, whether or not they have physical bodies. It is a popular tattoo because it has many different meanings, and it relates to just about every religion and culture in some way.