When there is attraction between two Sims, each gets a buff if they're in the same room together.Also, all Romantic-type social interactions between the two have a slightly higher chance of succeeeding, and the relationship score between the two will climb slightly faster.Attraction is subject to the same rules as other relationships when considering whether men or women hit on any particular Sim.
Other Sims don't respect your vows, so you may get a lot of calls asking your Sims on a date even if they're married.
There is no way to turn it off (unlike opportunities), so it might get a little annoying if your Sims have particularly active social lives.
As you can see in the screen shot here, a townie is attracted to Pete simply because she caught him studying a new skill.
Attraction can occur for any number of reasons, though you'll likely see it most often when Sims learn new skills.
It's a small mechanic, but it can give your single Sims a romantic target in case you have no other plans.