1845, "animal which browses," agent noun from browse (v.). From 1863 as "person who browses" among books. In the computer sense by 1982.
The first browser was invented at PARC by Larry Tesler, now a designer at Apple Computer. Tesler's first Smalltalk browser was a tree-structured device. It enabled programmers to hunt quickly for items in a Smalltalk dictionary. [InfoWorld magazine, vol. v, no. 4, Jan. 24, 1983]