It's apart of the attraction system that came with the Generations patch, if I remember correctly.
I don't think she can personally send gifts through the mail. She'd need to do that in person by having the gift in her personal inventory and then gifting it to the guy Sim.
Click on Sim you want to gift to and select Friendly > Give Gift - then select something out of the list shown.
Depending on the options, the path may be Friendly > More > Gift Gift