I find it hard to translate it in English too and I try to adapt it to each context. The word basically means "to introduce". For example, if you buy a bag of chips and you want to eat the chips, you introduce your hand into the bag: "bagi mână în pungă". It is usually used when talking informal. For instance, you could be polite when you go to a bank and say that you want to deposit money and say that "aş dori să depun banii în bancă", and then go to your friends and tell them "am băgat bani la bancă". It is also used in swear expressions, such as "Îmi bag picioarele" (that's the pretty version). You could write here some examples of where you saw it. :)