a vague (something)

"Vague" means "not clear". Here are some things that can be called vague:

I felt a vague sense of disappointment when I heard about that.

He gave a vague explanation of how it works.

Politicians always make vague promises to improve this and that around election time, but they rarely follow through.

have an (adjective) understanding of (something)

You can use this phrase to describe how well you understand something. It's an intelligent-sounding phrase. In the situation above, you could also say:

I don't know much about Korean politics.

But this version doesn't make you sound as intelligent as the original version.

Other adjectives that you can use with "have a ___ understanding of ___" include:

She'll probably have a better understanding of what's going on.

We now have a deeper understanding of the ecological effects of greenhouse gasses.

We want to make sure that all students have a basic understanding of Algebra.