After it had passed, they swam on as quickly as they could because they knew that the boat would soon return.
Can I replace ‘swam on’ with ‘swam’? What is the difference between ‘swam on’ and ‘swam’?
To [verb] on means to continue to [verb], generally in the same manner or direction as you were before.1
Thus, to swim on means to keep on swimming, probably in the same direction as they were before. In this case, it indicates that they didn't stop (or remain stopped), or turn back or divert their course. That conveys additional meaning that would not be there if it were just swam without on.
Note, however, that on can also be a preposition for an adverbial phrase. "I walked on the path" is not walk on, but walk with an adverbial of location.
1: There are exceptions, such as carry on which is really a phrasal verb that connotes a more general meaning along the lines of the above without being specific about what is to be continued.