A tab is a small flap or strip on an object. In the case of books, they're used for easy identification or reference (eg. in a filing system). So I suppose to keep a figurative "tab" on someone is about gaining information on them for later reference.

keep tabs on someone/something 1. to keep a record on something or someone 2. to watch someone or something carefully

to keep a tab on sb/sth (american version) = to watch something or someone carefully Tab = tag or label = 标签