Punctuality is important because it is polite to be on time. Being late to an appointment or event is simply rude. Lateness leaves a bad impression.
Being late leaves the impression that a person is irresponsible or unprofessional. This bad impression can impact both current work and future employment prospects. On a personal level chronic lateness can strain relationships and cause other people to have to readjust their schedules accordingly.
As a general rule, it is far better to show up 10 minutes early than it is to be even five minutes late. Punctual people are seen as trustworthy; chronically late people are not.