Break-in or QSK is an operational mode that requires particular hardware enabling its user to listen while transmitting Morse code. The receiver is open in the pauses between the dashes and dots of a Morse letter. This requires either a fast transmit/receive switch or a separate receiver with a separated receiving antenna sufficiently isolated from the transmit antenna.
If it is possible to have an open receiver only in the pauses between letters, we speak of semi bk or semi QSK.
Full break-in traffic is one of the most advanced uses of CW, in the old times (when RX and TX used to be separated) it was pretty common. With the upcoming commercial rigs in the 60ies and 70ies the use of QSK dropped a lot. Yet, high-end transceivers may have useful QSK. Progress in electronics made QSK more affordable, yet, only a few operators do use it all the time. Those who do are convinced that QSL operation is the best what you can get out of CW.
a final BK often means something like "back to you, but please do not bother to repeat the call signs now". It is meant to ask the qso partner a quick question. With this meaning it is usually given as -... -.- with the space between B and K.
Yet, the literal meaning of bk is that the op is fit to operate in QSK mode.