Apple Pay is more secure than using your credit card because it uses NFC (near field communication). Every time you pay, it generates a unique code that cannot be used again. That is in contrast to using your credit card where you have that little extra 3 or 4 digit code in addition to the credit card number.
I found a quick useful article, Apple Pay Do's and Don'ts at http://www.forbes.com/sites/paularosenblum/2014/10/21/apple-pay-dos-and-donts-a-practical-guide/
Another good article about it from CNET, Everything You want to Know About Apple Pay is at http://www.cnet.com/news/everything-you-want-to-know-about-apple-pay/