I think they mean memorize. Most students simply lack the mathematical experience to internalize a definition correctly without simply memorizing it. They will

I think they mean memorize. Most students simply lack the mathematical experience to internalize a definition correctly without simply memorizing it. They will forget an "only if", or accidentally swap two quantifiers around, or conflate two variables that need to be kept separate, etc. This is okay! They're students on the way to gain that experience. At some point you can and will go over to internalizing, instead. But as advice to students just starting out, memorizing is the way to go.