How humans evolved to have head / beard hair that continues to grow longer than other animals is a topic that many anthropologists & biologists are still not sure about & there is no general consensus as to "why" yet.
The three main views that I am aware of however are :
1) Evolution of the "Aquatic Ape." (Ingram, 2000: Morgan 1997; 1982)
- Infants, in order to hold onto their mothers in the water, would latch onto her hair. Limiting separation from the mother & increasing chances of survivability
- Longer hair meant that infants / small children would need to swim less in order to get to their mother
- Believed to be supported even further when you consider that aquatic mammals are almost always hairless, indicating that at one point, humans were highly "aquatic" mammals.
2) No real benefit, but used as a tool for "mate selection." (Darwin, 1871; Cooper 1971)
The view held by many of the Darwin school of thought (I do not mean that as a derogatory), is that at first, "hairiness" was sexually attractive, but eventually "hairlessness" became more sexually attractive in most places (i.e. the face to see facial expressions & socialize better; Wong & Simmons 2001)
A sign of "virility" & "health" as can be seen in the mate-selection behavior of lions. Which is true even today as human diagnostic material for health (Klevay, 1972).
3) Practical evolutionary benefits for the human species specifically
A lot of body heat escapes from the head, probably the most important part of your body. Hair is a good insulator that can keep in heat. This increases survivability in colder climates. (Wong & Simmons 2001; Bubenick 2003). (A disputed but considered credible reason, especially when you compare hair length and types across different regions throughout history)
Protection against damaging UV rays (while still permitting adequate Vit.D3 to come through) & some protection from free-radicals or other harmful particles. Because we became bi-pedal, the head was the main area exposed to the sun (as well as some of our back). Extending hair's usefulness to even hot environments, while other body hair became less important with the development of sweat glands (Wheeler 1985).
Heightened "Situational Awareness" through "Touch sense." A concept that may seem silly at first but has some evidence to support the theory. Though the hair is not "alive," it is connected to the follicles & your nerves. In a nutshell, it may help to increase "sensory awareness" & "data gathering" of your environment, which would favor longer hair. This would be an asset in survivability (Kardong 2002; keratin.com 2010; Sabah 1974; washington.edu)
Though not a collegiate Journal article, if reasonably credible, this small article is an interesting case for supporting hair & "Touch sense" in "recent history" & in combat-survival : http://www.sott.net/article/234783-The-Truth-About-Hair-and-Why-Indians-Would-Keep-Their-Hair-Long.
I personally lean 90% "Evolutionary benefits" & 10% "Mate selection" as to reasons why humans' hair continues to grow longer than other animals. Beard & head.
Hope this info was a little helpful. There are copious amounts of other respectable articles on each point, but I only referenced a few.