Entender and comprender both mean "to understand". They are interchangeable. However there is a subtle difference between them. Despite sharing the same meaning, we will use "comprender" to express a "deeper understanding";by this I mean, to understand the implications of what someone says, i.e. what is beyond what is said.
If I say something in Spanish to an English speaker for example, after saying it, I could add the question "¿Me entiendes?" (Do you understand me?) With this question I simply want to know whether the English person has understood the words I just said.
If I am telling someone an anecdote, a problem, an opinion...I could add at the end the question "¿Me comprendes?" (Do you understand me?) With this question, more than wanting to know if my friend has heard and understood correctly what I just said, what I want to know is if my friend understands and is getting my message, the implications of what I just told him/her, if he/she really understands why I did what I did, etc. It is a deeper understanding with comprender.
Having said that, to be honest, we do mix them up and sometimes we actually use entender when we "should" be using comprender in the sort of situation that I just described. So you are quite safe interchanging them.
I hope this helps.
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