It means that he takes credit for your work. For example when you do something good, he doesn't say that you did it. Instead, he claims that he's the one who made it happen.

There is also a meaning, depending on context, that he doesn't believe IN you. If people are wondering how a girl will make a trip by herself, someone could say, "They don't give her much credit. She could do that easily." So not believing someone could do well is not giving them credit, if it's not actually a problem for them.

give credit = give a good rating It can be used in almost ANY situation where something has to be rated. Believability can be rated, so you can use it there.

It means 'he' doesn't really believe/espouse that you contributed to the completion or success of an endeavor. e.g.: You and a schoolmate are working on a project, and you both read and write 50% of the final draft. However, when speaking to other people, your schoolmate says 'he helped a little, but not that much.' In this case, he 'would not be giving much credit to you.'