As Qasem said, they all essentially have the same meaning but 'understand' is most commonly used.
There are small differences - take these examples whereby you are responding to someone who is debating something with you:
- I can't understand what you are saying (you are speaking to quickly, you have a strange accent)
- I can't comprehend what you are saying (I can 'understand' what you are saying, but I disagree with your argument)
- I can't grasp what you are saying (I can 'understand' what you are saying, I do not disagree, but I cannot understand the content of your argument)
Overall, they are very similar and you will be fine saying either. The above is just small nuances that you will only encounter very rarely!