It means the person thinks/believes that they are very good and fast at learning new things. They are combing two idioms together. "to be quick on your feet" = to be able to react quickly to situations and emergencies, without panicking etc. "to be a quick learner" = a person whoo seems to be able to learn things without having to study a lot, has a good memory and recall. examples, at the scene of an accident there are people who react quickly and do the right thing, and there are people who freeze and become helpless and hopeless. A person fast on their feet will be able to seize life's opportunities, they react quickly instead of delaying and procrastinating. Other people will "let the grass grow under their feet" = opposite of "quick on their feet" they are slow and miss opportunities. "very sorry Mr Smith, you are too late the job has been taken we had three applicants yesterday, you should have contacted us as soon as you received our letter". "A quick learner" able to solve problems quickly and to adjust quickly.