Just a few of the benefits of a vigorous, uncovered boil:
-Extracts, isomerizes and dissolves the hop α-acids
-Stops enzymatic activity
-Kills bacteria, fungi, and wild yeast
-Coagulates undesired proteins and polyphenols in the hot break
-Evaporates undesirable harsh hop oils, sulfur compounds, ketones, and esters.
-Promotes the formation of melanoidins and caramelizes some of the wort sugars (although not desirable in all styles)
-Evaporates water vapor, condensing the wort to the proper volume and gravity (this is not a primary reason, it's a side effect of the process)
-Drive off DMS.
-Prevents boilovers.
-Concentrates wort.
-Bind hop compounds to polypeptides, forming colloids that remain in the beer and help form a good stable head
-Lowers pH in order for proper cold break to form and fermentation to proceed normally.