block (n.)
"solid piece," c.1300, from Old French bloc "log, block" of wood (13c.), via Middle Dutch bloc "trunk of a tree" or Old High German bloh, from a common Germanic source, from PIE *bhlugo-, from *bhelg- "a thick plank, beam" (see balk).

Meaning "mould for a hat" is from 1570s. Slang sense of "head" is from 1630s. Extended sense of "obstruction" is first recorded 1640s. In cricket from 1825; in U.S. football from 1912. The meaning in city block is 1796, from the notion of a "compact mass" of buildings; slang meaning "fashionable promenade" is 1869.
BLOCK. A term applied in America to a square mass of houses included between four streets. It is a very useful one. [Bartlett]
block (v.)
"obstruct," 1590s, from French bloquer "to block, stop up," from Old French bloc (see block (n.)). Meaning "to make smooth or to give shape on a block" is from 1620s. Stage and theater sense is from 1961. Sense in cricket is from 1772; in U.S. football from 1889. Related: Blocked; blocking.