Here's a response from Ed Stark, creative director for D&D Core:
The "typical" number of players in a group is 4.
The typical amount of time a game session lasts is around 4 hours of gaming time.
Players play on average, once a week.
An encounter of the PCs' level, plus roleplaying, can usually be resolved in around an hour or so. Four such encounters drains the PCs to the point at which they need/want to rest.
Character resting or "down time" (time for characters to rest and recuperate) is a good time to award experience and break the session. If you have too much down time during a session, there's less gaming and more bookkeeping.
If players play once a week and follow this pattern, they'll get roughly 16 encounters of their level every four weeks. They should "level up" once a month (with some room to spare for characters that die, or slow/abbreviated sessions, or whatever) so that they feel they're accomplishing something and getting better. That means that every two months they've gone up a little more than two levels.
And a shorter response from Jonathan Tweet:
We wanted XP level breaks to be divisible by 1,000 because that's simpler.
We wanted the standard encounter to be worth 300 times the encounter level because 300 is divisible evenly whether you have 2, 3, 4, 5, or 6 PCs in the party. Also, 300 gives you about the right level speed (as Ed pointed out).
That's why it doesn't come out to some nice, even number of encounters per level (because 300 doesn't fit into 1,000 nicely).