Can't means can not For Example: "I can't go to the movies because I have alot of homework to do." or "I can't figure out the answer to this question." Can't mainly expresses what you are not able to do. Couldn't means could not For Example: "I couldn't check the mail because I was late for work." or " I couldn't buy the book I wanted because I was out of money." Couldn't expresses things that you would not have time to do that you would normally do. I hope I was helpful.

Can't = Can not Couldn't = Could not "can" is easy to understand. very simple. same as 可以。 "could" has more specialized meanings － It can mean past tense (I could hear you on the phone), and it could also mean conditional tense ("I could go if I wanted"), it could also be used in a polite question ("Could you please do this?"_ here are some good examples for you: http://www.examda.com/cet3/fuxi/Grammar/20100430/104028260.html