Since I've recently made an attempt to describe jigs and hornpipes, I may as well deal with The Reel as well. But I'm going to take the easy way out by relying on Wikipedia and YouTube. I post it because it completes a train of thought, and there might be a few who would like to know.
A description of the reel from Wikipedia
Reel music is transcribed in 4/4, 2/2, or 2/4 time signature. All reels have the same structure, consisting largely of quaver movement with an accent on the first and third beats of the bar. A reel is distinguished from a hornpipe by consisting primarily of even beats. Reels usually have two parts (A and B); in most reels each part is repeated (AABB), but in others it is not (ABAB). Each part (A and B) typically has eight bars, which in turn are divisible into four-bar and two-bar phrases. The structure follows a scheme of question-answer, where the first phrase is the "question" and the second is the "answer." The group of thirty-two bars (four times eight) is itself repeated three or four times before a second reel is introduced. The grouping of two or more tunes in medleys or "sets" is typical in Celtic dance music. Today many Irish reels are supplemented with new compositions and by tunes from other traditions which are easily adapted as reels. It is the most popular tune-type within the Irish dance music tradition.
Reels are popular in the folk music of South West England. It crossed the Atlantic ocean with Irish and British immigration and thus entered the musical tradition of Atlantic and French-speaking Canada including that of Quebecers and Acadians. Reels are featured in many pieces of Quebec singers and bands; for example: La Bolduc, La Bottine Souriante and even the more modern néo-trad group Les Cowboys Fringants (like the song Mon Pays suivi du Reel des aristocrates).
A sample of the music and dance from YouTube