You're looking for a controlled, vigorous, rolling boil. A simmer won't accomplish some goals, while a roiling, angry boil can over accomplish others.
Boiling wort accomplishes a number of important tasks for the brewer. It should be given due time to accomplish these tasks, no more and no less. 60 to 90 minutes is the right amount of time to accomplish all tasks, depending on the brewer's goals.
Concentration. Boiling creates steam. Steam is excess water being driven off and the resulting wort will have a higher gravity than it began with. Concentration allow the brewer to fully sparge sugars from the grain with enough water to allow for boil time and reducing it all to the correct volume and gravity.
Sterilize. A boil of at least 20 minutes achieves a reliable degree of sanitation. Continued boiling increases the sanitation into sterilization. The clean, sterile wort is enhanced by a rapid chill to fermentation temperature This leaves a pristine environment for yeast to be added quickly and ferment without competition. No known pathogens can survive even a minor amount of fermentation, therefore a clean wort leads to a clean beer.
Volatilize. Here we get into one of the most important reasons for extending boil time. Pale malts produce Dimethyl Sulfide (DMS), a sulfur compound most readily identified as canned corn. DMS is produced throughout the whole hot cycle of brewing (mash and boil) and volatilized through a vigorous boil. Paler malts have more DMS, while malts above 6 lovibond generally have very little to none because it's driven off in kilning. In a properly conducted boil, DMS is driven to below the threshold of perception between 60 and 90 minutes.
Stabilize. Malt contains not only sugars, but important yeast nutrients, minerals, amino acids, enzymes and proteins. Some of these we need, while others are in excess and should be reduced. Enzymes are a major part of mashing, and boiling stops any remaining action that the brewer didn't finish. The major stabilization is with breaking proteins out of suspension. Proteins create viscosity, which is appreciated as part of body and head retention. However, too much leaves a slick, oily feeling, akin to freshly cooked breakfast oats. Additionally, proteins create haziness in beer which is undesirable in most styles. Hot break is accomplished in the forst 15 to 30 minutes of boiling. Cold break is a result of the shock from rapid chilling wort from boiling to pitching temperature; the faster the better.
Isomerize. Hop bitterness is part of balancing beer's residual sugars after fermentation. Permanent bitterness is achieved when hop alpha acids are isomerized into a permanent form. Isomerization is not a linear scale. Most isomerization happens in the first 15 to 30 minutes, then it slows dramatically. Nearly all isomerization is complete at about 60 minutes, with only modest gains after that.
Caramelize. In most home brewing rigs, a flame is used to generate the boil. Over time, the heat can caramelize some sugars, carbohydrates and proteins via the Maillard reaction. The result can be deepened color and richer malt flavor, or can be scorched and smokey.
