A modal verb is a helping verb. In English, "modal" is related to the word "mode", which means, the way something is done. Modal verbs in English help the main verb to express not so much what is done, but how it is done.
In this way modal verbs are much like adverbs. Adverbs also modify or describe the action of the verb. But a modal verb is able to stand on it's own, to form a complete sentence. The main verb used with the modal verb, also does not change in fo
rm. Modal verbs are used to give a polite answer to questions. Can you lift this box for me? Yes, I can. To say Yes, I can is more polite than to simply answer, Yes
Can: expresses the ability to do something. "I can carry that heavy box by myself." (to say that it is possible for him to carry out the task)
COULD: is used to express probability, and also to make suggestions.
MAY: is used to express the possibility of something. He may know about our secret. (similar to might.)
MIGHT: is used to express the possibility of something. He might know about our secret. (similar to May.)
MUST: expresses the need of doing the thing. "You must call your mother, I heard that she is felling sick." (used for advising somebody, indirectly commanding him to do it)
SHOULD: expresses that something is necessary. It is used in either giving or asking advice. "You should call your mother, and find out how she is doing". (Giving) "Should I call my mother, and find out how she is doing?" (Asking)
WILL: expresses the confidence in one's speech "He will definitely finish the work by tomorrow."
WOULD: expresses possibility. 'If I were King, I would rule graciously.'
There are rules of using these Modal verbs, there is a video showing how it should be properly used.