Matthew Arnold was an English poet and cultural critic who is often regarded as the first modern critic in literature. He introduced his touchstone method of criticism in his most popular essay, "The Study of Poetry." The method is essentially a comparative study of older, classic poetic masterpieces and newer contemporary works of poetry.
In order to properly analyze, judge, and criticize a literary work, the critic should first take a few lines of poetry of the great poetic works written by the masters of poetry and literature (such as the Ancient Greek writers, Shakespeare, or Milton) and then compare these well-known literary works to the new literary work he/she is examining. This way, the critic can determine whether or not a literary work is good or bad.
The touchstone method of criticism helps the critic get rid of potential biases (both personal and historical) and to make an objective, impersonal, and unbiased judgement. If critics are incapable of differentiating between objectively good and bad literature, then literature itself is in danger of losing its real value, which is the main reason why Arnold came up with the touchstone method.
Some critics support and use Arnold's touchstone method of criticism, deeming it logical and creative, but some find it a bit too limited, as one writer's imagination, creativity, and skill can be completely different from another and shouldn't be compared, nor should their works be judged by just a few lines of poetry or prose.
You can find more information about Matthew Arnold, his ideas and theories on literary criticism, and his famous touchstone method of criticism here.