The purpose of transitional words is to connect ideas, sentences, and paragraphs in any piece of writing or speeches in order to make the ideas flow smoothly and better.
There are a variety of transitional words and each of them have a role: some are used to express contrast (like on the contrary, however, notwithstanding), others to denote time (after, at last, before), to add more information to a previous point (furthermore, besides, moreover), to show similarity (likewise, similarly, in like fashion), to illustrate a point or give examples (for instance, for example, to illustrate), etc.