Of the best quality; of the highest social standing.
The 'drawer' in question here is the highest drawer of a bedroom chest of drawers. This was where Victorian gentry kept their most valuable items - jewelry, best clothes etc. The phrase 'top-drawer' was initially used to denote a person's level of social standing, based on their family background. Families were either 'top-drawer' or they weren't.
The earliest citation of the phrase that I can find comes from the English writer Horace Vachell, in the novel The hill, a romance of friendship, 1905:
"You'll find plenty of fellows abusing Harrow," he said quietly; "but take it from me, that the fault lies not in Harrow, but in them. Such boys, as a rule, do not come out of the top drawer."
See also: top notch.