1510s, "purpose, design," from Latin institutum "an ordinance; a purpose; a custom; precedents; principal components," literally "thing set up," noun use of neuter past participle of instituere "to set up, put in place; arrange; found, establish" (see institute (v.)).
From 1540s in English as "an established law." The sense of "an organization or society devoted to some specific work," especially literary or scientific, is from 1828, from French use in Institut national des Sciences et des Arts (established 1795); Dutch instituut, German Institut also are from French. The specialized (mostly U.S.) sense "traveling academy for teachers in a district" is from 1839.
A "Teachers' Institute" is a meeting composed of teachers of Common Schools, assembled for the purpose of improvement in the studies they are to teach, and in the principles by which they are to govern. It is the design of a Teachers' Institute to bring together those who are actually engaged in teaching Common Schools, or who propose to become so, in order that they may be formed into classes and that these classes, under able instructers, may be exercised, questioned and drilled, in the same manner that the classes of a good Common School are exercised, questioned and drilled. [Horace Mann, secretary's report to the Boston Board of Education, Sept. 1, 1845]