There are things you can do with a storyboard that you can't do with a nib. A storyboard lets you create segues between view controllers, and it lets you design table view cells in-place.
There are things you can do with a nib that you can't do with a storyboard. In a nib, you can create references to the File's Owner placeholder. You can create multiple top-level views, edit them, and create connections between them. See this answer for an example of why you'd want to do that. You can add external object placeholders (a rarely-used feature).
Storyboards have the drawback that they collect a bunch of different, loosely-related objects into one big file. If you're working on a project with several developers, you are much more likely to run into merge conflicts if you're using a storyboard than if you're using xib files.
You should definitely learn about nibs at some point. Whether you want to start with them or start with a storyboard is probably not too important. Just find some tutorials you like and work through them with whichever type of file (nib or storyboard) they use.