A verified account is usually awarded to someone who is a legitmate member of the community. Verification is a label they receive as a token of identification of their presence and contributions to the community.
A verified account is usually differentiable by blue checkmark. Anyone with a verified account is looked upon by the community as an integral part of it.
Another important aspect of a verified account is to avoid identity theft or misrepresentation of a someone immitating be someone else.