When you latch on to something, you attach yourself to it. You can latch on to your friend by grabbing her arm, or you can latch on to a trend by enthusiastically following it.
When your sister latches on to a new hat craze, she'll buy a bagful of berets and fedoras and wear one to school every single day. And if you latch on to a new health regimen, you may annoy your family by throwing out everything in the house with sugar in it. When you latch on to a person, it's often unwelcome to them: "My little brother latched on to my friends, so we jumped on our bikes and rode away."