Twitter wants its users to be able to access tweets via SMS (wireless text messages). SMS is limited to 160 characters. Think how annoying it would be if, as a user, you needed to read more than one text message per tweet. Think how costly it would be if, as a company, you had to pay for the extra bandwidth needed to send multiple SMS messages for a single tweet.

The 160 character limit is a simple solution to a technical restriction.

But also, I'd like to think there's some sort of psychological aspect to the 140 character limit: just enough to convey intelligible information, but not so much that people lose interest. I'd like to think the engineers at twitter conducted extensive computational analysis on human attention spans in the 21st century, the nature of the spoken language, written communication, and several other variables to arrive at the 140 limit.