It's just as vague as in English... it's a literal translation. There are interpretations to "a soul is cut off" from its people, but literally it means not more that this.

I agree with Natã, the meaning is in most cases to be expelled from the family or from the People of Israel. The sages of the Mishna and the Talmud also speak of a sudden death (or a death at young age) in this world or the fact that those offenders will not be part of the afterlife (העולם הבא) It does not mean to execute the person who has broken the law.

When you see the verb CUT in the Bible it's usually related to a contract or a pact being established. Like the Abraham's pact at the beginning (Genesis). Now, when the expression "cut off", as you asked, comes in, it's like the contract is being broken, this contract is related to God's pact with Israel. When it is broken in some severe manner, the perpetrator is expelled from the people of Israel. I hope I helped in some way. ;)