What is the exact meaning and etymology of 拜年？
When Chinese new year comes, families will go out to visit their relatives, friends or seniorities. According to this page from Baidu Encyclopedia, at earlier time, the kids should kowtow(叩头, the same as 拜) to salute. In return, the elders will give them pocket money in red envelop. Nowadays kids don't have to kneel, but pocket money is still a tradition.

And you can say "pay a New Year call" in English.