Many questions occur. Why is it more convenient to apply for credit card online? How safe is it? Etc, etc, etc. I believe the reasonable answer is quickness and easiness. Everything that you should do-switch your PC and find the right site with convenient charts for credit card comparison. If you know for sure what your credit score is, it will be not difficult to choose the suitable credit card deals section and card itself. Weigh pros and cons of each offer!
It is really safe because all required personal data you send goes directly to the credit card company you have chosen through safe & secure (SSL) channels. I think it is also a good way to save time.