Generally, I see "continue" (and "break") as a warning that the code might use some refactoring, especially if the 'while' or 'for' loop declaration isn't immediately in sight. The same is true for 'return' in the middle of a method, but for a slightly different reason.
As others have already said, "continue" moves along to the next iteration of the loop, while "break" moves out of the enclosing loop.
These can be maintenance timebombs because there is no immediate link between the "continue"/"break" and the loop it is continuing/breaking other than context; add an inner loop or move the "guts" of the loop into a separate method and you have a hidden effect of the continue/break failing.
IMHO, it's best to use them as a measure of last resort, and then to make sure their use is grouped together tightly at the start or end of the loop so that the next developer can see the "bounds" of the loop in one screen.
"continue", "break", and "return" (other than the One True Return at the end of your method) all fall into the general category of "hidden GOTOs". They place loop and function control in unexpected places, which then eventually causes bugs.