Generally background checks are done mainly for the purposes of screening potential
employees when applying for a job which may require a particular position of trust, for example handling large sums of money or being responsible for the safety of other people. They generally involve looking up the persons criminal and financial records although in some cases medical histories are also important if you need to have a certain level of fitness to perform the job capably. And of course there is the whole working with children and sex offenders issue which is a bit of a no brainer. There are other things that make background checks absolutely necessary generally these are things like the legal eligibility to work in the country amongst other things.
There have been an increasing number of background checks requested personally by people for somebody they have met, perhaps a new neighbour or a potential partner. You can never tell what someone is hiding seems to be the vibe that has cropped up into modern society which has caused this increase in mistrust and ultimately people requesting background checks. These sorts of checks can in many cases be considered unlawful in certain countries particularly in UK law due not only for the potential of identity theft, but also as a breach of privacy.
The most common use of these checks will likely always remain for employment although the growth in the market outside of employment related checks is quite considerable with more people becoming increasingly suspicious of the world around them it is hardly very surprising.