Party Level is a concept dating back to the late 1970's - in general, tho', it was popularized in D&D 3E (where it hit a form close to that used in 4E). The term Total Party Level is used in Alston's D&D Cyclopedia (pg. 100-101), and isn't an average, but is the first formal rules inclusion I can find.
While not explicitly defined in 4E PHB1, DMG1, nor MM1, it's used in DMG 1 in the section on encounter balancing. DMG page 31 notes the "default size" of a 4E party is 4-6 players, and that encounters should be based upon this.
Given that 4E also presumes player characters will adventure in groups of the same level, and will level up at the same time, no math was expected to be needed.
So, generally, a balanced encounter is a number of monsters equal to the number of PC's, and of the same level as the party average level. (See 4e DMG p 104 for variations on this.)
But in prior editions, it was forumlaic. 3.0 and 3.5 used the explicit average of PC's levels. As noted before, Cyclopedia used the total level of the party members, rather than an average.
Why it's useful
The party level is used to determine what a "suitable threat" is for the party. An encounter with a single opponent of a threat level equal to the party level should be a "fair fight" - which means, the players are likely to win, but expend a reasonable portion of their expendables, including HP and ammunition.
In general, such balance is only for those who treat the game as a form of miniatures gaming; as one gets into story mode, balance (and party-level based calculations) become less important.