It means to be rational, to be understandable.
"The coach said we're not going to work on our backhand for two weeks."
"That makes sense; it's a good idea to work on a strong forehand first." [n.b., I know nothing about tennis, this might be completely false:)]
"John said he'll be there Saturday night."
"That doesn't make sense---he told me he had to go out of town this weekend."
"He said his trip was cancelled. The software isn't ready for demonstration yet."
"I see. There's no sense in flying down there to demonstrate a half-baked product."
Student or Learner