The Social Security Number (SSN) is a number given by the US government to citizens, which is used for purposed that have something to do with the Social Security System. For example, one purpose of the SSN is to keep track of the taxes paid by citizens.
Yes, you can. If you are foreign you can ask for your US Social Security Number, something that is needed if you want to start a new job.
If you don’t want to get a job in the US, you do not need it. However, if you want to start a new job, you must ask for a SSN. Without SSN, you cannot obtain a job in the US.