Its like a symbolism. Angelitos (Little Angels), is the term used for the Dominican Republic Christmas tradition of exchanging small presents between friends or work colleagues. The names of all people involved are written on small papers which are then put in a basket. Everyone will pick up one name and consequently become their 'little angel' responsible for 'secretly' buying them a present!.
The Dominican Christmas tradition of 'Angelitos' can start, for example, two weeks before Christmas, having as many exchanges per week as the group wants. People are not allowed to know who their angels are. All the fun is, precisely, to try to 'discover' who is your 'angel', without giving yourself away. People will try to give false clues about who's 'angel' they really are. On the final day for giving presents, people will give a nice present to their angels as well as revealing their 'real' identities and, of course, everyone has a nice party to celebrate it!