Soulmates are two people who are in true love. Destined for each other. Two halves of the same soul, to quote Nobby Nobbs. Usually there's lots of character development, plot, obvious attraction and plot tension to illustrate how good they are for each other. In the case of badfic, 'soulmates' means 'don't you think they look CUTE together?!'
Abuse of the concept of soulmates is a chargeable offence, and is usually seen when a Sue is thrown into a soulmate bond of some sort with a Canon character with practically no justification whatsoever. Agents from species that invest great importance in romantic relationships can take soulmate abuse quite seriously; one notable group of races that reacts this way are Tolkien Elves, whose marriage customs involve a union of souls. One of their number, Agent Eledhwen Elerossiel, has been especially prone to soulmate-based rage after a set of dire BBC Sherlock missions.