You should understand what's going on, to a degree. It doesn't hurt to know what's underneath, but sometimes that's not optimal to know everything either, for example: is .innerHTML consistent? Not completely, e.g. <select> in IE. Does that mean you need to know every inconsistency? Not if you're letting jQuery handle it.
People say you need to understand JavaScript before jQuery, let me say I agree, however there are limits to that though, you don't necessarily need to know every quirk and inconsistency between browsers for example, that's why we use an abstraction layer.
To me, this is no different than saying you need to learn assembly before C#, should you know what's happening, how memory is referenced, what a pointer is? I think so, do you need to know every detail? Probably not. We would never progress if every new programmer goes through learning every layer beneath, this is why math theorems build upon others known to be true, same concept.
You should be able to trust your abstraction layer. Is this always true? unfortunately not, but jQuery does a pretty good job at being as consistent as possible and always improving. More importantly, the community does a good job of making the inconsistencies known.
Edit: Let me caveat everything above by saying if you can learn what's underneath do so (this applies to most any abstraction in my book, not just JavaScript), it will help you program better and more efficiently. If you know what's going on under the covers, you can more optimally take advantage of it.