For me, "understanding" and "comprehension" are mostly synonymous - they usually mean the same thing (with a little nuance (: of course ). But, use of the word "comprehension" is less common in conversation, and it is usually reserved for describing how well someone knows a subject matter like mathematics or a foreign language, for instance
"My English listening comprehension needs work. I'm not good enough at it yet!" - (Sounds good)
"My English understanding needs work." - (Sounds a bit awkward)
If someone has good listening comprehension, it means that they usually understand what others are saying VERY well.
I can understand what someone is saying to me - I hear their words and I can process their meaning. But, if I comprehend what someone is saying to me, it usually indicates that you have a deeper or more thorough understanding of what they said.
You can "understand" what someone says, but you can "comprehend" the other meanings, consequences, or importance of their words.