What is the function of a topic sentence?

The topic sentence is a primarily prescriptive grammatical term to describe what is usually, but not always, the first sentence in a paragraph. The topic sentence acts as a kind of summary and offers the reader an insightful view of the writer's main ideas for the following paragraph. More than just being a mere summary, however, a topic sentence often provides a claim or an insight directly or indirectly related to the thesis. It adds cohesion to a paper and helps organize ideas both within the paragraph and the whole body of work at large.