Continuity of a circuit is it being tested from one place to another to prove its a complete circuit and not showing a break or open circuit. i.e. it has continuity (or is continuous). A buzzer will sound too - assuming the meter has this option, if continuity is good.
Turn meter dial to its Ohms range (any will do) and then with the test leads touched together the meter will read 0.1 or less Ohm depending on scale used. This is checking the continuity of the meter leads. If say one lead was broken a high reading or Open circuit reading would be shown the same as when Ohms range is selected and the meter leads are apart. Open Circuit has no continuity. If the broken lead was partly broken through and at the break the two ends were just touching you may well read a high resistance on the meter but possibly not a full short reading This is called a High Resistance joint or connection.
A good meter usage test I used to get my new apprentices to do was to read the values of some resistors. I used 10, 100, 1000, 10,000 100,000 and 1 Million Ohm resistors and they had to check them and advise me which were which using the multimeter they had also set up (on its appropriate Ohm range for starers). Often the newest ones were thrown by the meter showing say 990 Ohm for a 1000 Ohm resistor
BTW. Two things that must always be done .... Always turn a meter Off after testing. If you have been using the Amps (Current) ranges replace the red lead back into the Volts/Ohm etc socket. Never leave the red lead in the Amps or milliamps socket once you've finished current testing.
