The term is also synonymous with "coppertop" (a reference to the "Duracell" brand of disposable chemical batteries and an inference to a pod-human's primary use: power generation for the Machines).
The term gets its name from the color of one of two virtual pills offered by a hovercraft operative (who has rematerialized inside the Matrix as an avatar) to a human still living out a life within the Matrix. If the human chooses to continue their life within the Matrix, the virtual blue pill presumably contains a reset command that sends the human back to his home to continue his existence within the Matrix, and completely forget anything about the conversation.
Of all of Zion's inhabitants, only humans who are born within the Matrix can become operatives that can reenter the Matrix, as they have the headjack that allows their minds to be retransmitted back into the Matrix's broadcast network.
The opposite of a Bluepill is a Redpill.