Building societies are a form of financial mutual that is, in effect, a bank that is owned by its customers. The name reflects there origins, providing personal mortgage lending and savings accounts. They are similar to savings and loan associations in the US.
Building societies do have a good track record of providing good interest rates and low fees to customers. Given constraints on competition in personal banking (people are reluctant to move their accounts to get the best deal), they can be seen as providing a solution to conflicts of interest between banks and customers.
Current law is somewhat slanted against the continued existence of building societies, in that it is possible to demutualise them, converting to shareholder ownership. This produces a windfall for members, which in turn attracts "carpet bagging" members who join purely to benefit from the windfall and inevitably vote for demutualisation.
Most surviving building societies have devised defences against demutualisation, such as requiring new members to agree to donate the money they make from demutualisation to a charity. However, these restrictions cannot be applied to tradeable deferred shares, which, in practice, means PIBS.
Many building societies retain their historical strengths in mortgage lending and personal banking. They tend to be comparatively weak in business banking and similar areas. For this reason, some of those that have demutualised are sometimes called mortgage banks.