Full Idea
Trivially, the Identity of Indiscernibles says that two individuals, Castor and Pollux, cannot have all properties in common. For Castor must have the properties of being identical with Castor and not being identical with Pollux, which Pollux can't share.
Gist of Idea
An object is identical with itself, and no different indiscernible object can share that
Source
report of B Russell/AN Whitehead (Principia Mathematica [1913], I p.57) by Robert Merrihew Adams - Primitive Thisness and Primitive Identity 2
Book Reference
'Metaphysics - An Anthology', ed/tr. Sosa,E. /Kim,J. [Blackwell 1999], p.175
A Reaction
I suspect that either the property of being identical with itself is quite vacuous, or it is parasytic on primitive identity, or it is the criterion which is actually used to define identity. Either way, I don't find this claim very illuminating.