"I can't understand this word's meaning." Both are grammatically correct. In my opinion, "I don't understand this word's meaning." is more accurate. You don't understand it now, but would be able to understand it if it was explained to you. "I can't understand..." would be interpreted the same way as the first by most English speakers. However, logically, it implies that you are unable to understand it no matter how many explanations you get. It is a very minor difference, actually. Hope this doesn't confuse the issue.

I agree with fdmaxey. An even more standard way to express this would be I don't know this word or I don't know what this word means "Understand" seems to imply that you are engaging in more elaborate mental activity (though of course in verbal communication it can refer to clarity of communication).