If something is finished quickly or on time, then it's been done in a timely manner. Homework, thank-you notes, and your taxes are just a few things that you should complete in a timely manner.
Hear that clock ticking? That's the time limit for learning this word in a timely fashion. But the word timely isn't always about speed — being timely can also mean being well-timed or doing something at the most appropriate moment. If you're going for a job interview, it's important to make a timely arrival. And if you bump into friends just when they were wondering how you were doing, then you've made a timely appearance.