Answer: Both “Do you understand?” and “Did you understand?” are grammatically correct, but they are used in different contexts.
“Do you understand?” in the present tense, one has the use of this at this time, whereby one would like to know whether the other party does understand something at the very moment—or in other words, grasping it at this very time. It is common in a conversation or instruction where one checks whether there is immediate understanding or not.
“Did you understand?” in the past tense is a question asked by someone to know whether someone got something said or explained by them sometime in the past. The speaker will usually pose this question to the listener after giving some information or instructions in a bid to ascertain if the information given is well understood.
If you are trying to explain something at the moment and you wish to find out if the listener is getting what you are trying to put across, you ask, “Do you understand?” In case you have finished explaining something earlier and now you wanted to check if the listener had, in fact, understood what you had said, you would say, “Did you understand?”