block (v.1)
"obstruct, hinder passage from or to," 1590s, from French bloquer "to block, stop up," from Old French bloc "log, block of wood" (see block (n.1)). Compare Dutch blokkeren, German blockieren "to blockade." Sense in cricket is from 1772; in U.S. football, "stop or obstruct another player," from 1889. Related: Blocked; blocking.
block (n.2)
"obstruction," 1831, from block (v.1), also in part perhaps an extended sense of block (n.1). As a type of defensive shot in cricket, from 1825; in U.S. football, the act of obstructing another player, from 1912.
block (n.1)
"solid piece," early 14c., blok, blokke, "large solid piece of wood," usually with one or more plane faces, from Old French bloc "log, block" of wood (13c.), which is from a Germanic source such as Middle Dutch bloc "trunk of a tree," Old High German bloh, from PIE *bhlugo-, from *bhelg- "a thick plank, beam" (see balk (n.)).

Generalized by late 15c. to any solid piece. Meaning "solid mass of wood, the upper surface of which is used for some purpose" is from late 15c., originally the executioner's block where the condemned were beheaded. Meaning "stump where a slave stood to be sold at auction" is from 1842. Meaning "mold on which something is shaped, or placed to keep its shape," typically a hat or wig, is from 1570s; sense of "head" (generally disparaging) is from 1630s, perhaps an extension of this. To knock (someone's) block off "thrash, beat" is by 1923.

Meaning "grooved pulley in a wooden case" (used to transmit power and change the direction of motion by means of a rope) is from c. 1400. Hence block and tackle (1825; see tackle (n.)).

The meaning in city block is 1796, from the notion of a "compact mass" of buildings.
BLOCK. A term applied in America to a square mass of houses included between four streets. It is a very useful one. [Bartlett]
Later of a portion of a city enclosed by streets, whether built up or not.
block (v.2)
"make smooth or to give shape on a block," 1620s, from block (n.1). Meaning "form into a block" is by 1863; that of "strengthen or support by blocks" is from 1881. Theater sense "designate the position on stage of each actor in a scene" is by 1961. Sense in cricket is from 1772; in U.S. football from 1889. Related: Blocked; blocking.