A closed form is a differential form $\alpha$ such that $d\alpha = 0$. A differential form $\beta$ is exact iff there exists a differential form $\gamma$ such that $\beta = d\gamma$.
I for the life of me cannot remember which is which. I don't use differential forms on a regular enough basis to commit these to memory. I looked up the history of the terms, and there's an answer on MathOverflow, which unfortunately does not shed light on why they are called "closed" and "exact".
One useful mnemonic I found for exact is that in the exact case ($\beta = d \gamma)$, $\beta$ is "exactly" $d\gamma$.
I would like to know other ways to remember these.