Themes in The Love Song of J. Alfred Prufrock
This idea of being pinned to a wall recalls the imagery of crucifixion, in which Christ was nailed (or "pinned") to a cross. It's also reminiscent of butterfly and bug collections, where specimens are "pinned" to display boards. As a whole, this phrase is meant to suggest social anxiety and discomfort, which Prufrock feels whenever he's made to account for himself (his "days and ways").
One of the poem's central themes is social anxiety and how it affects Prufrock's ability to interact with those around him. This line, like the others in the tea scene, is indicative of the discomfort Prufrock feels in social situations and his belief that he needs to put on a "face" or mask in order to fit in or hide his true self from those around him. This also fits into the theme of otherness presented throughout the poem.