Mead sees the self as having two sides, the subject side (myself as active, doing, perceiving, experiencing, capable of choosing and acting) and the object side (myself as fact, as seen by others, as fixed in a role).
When I "see myself as others do" I am internalizing their view of me as object (I am an object in their world). I can start to understand how my actions (which I experience immediately as a subject) go out into the world and become objects for others to react to. By internalizing these things I can orient my actions socially - to get the reactions or make the impression that I want to.
For Mead, it is only by internalizing lots of others' views of me as object that I can generate enough of an internalized generalized other to be able to be competent in society. My "social self" comes into being when I've done this.