Intestacy is a legal word which means that somebody has dies and not left a will. If you die and you have made a will, your will determines where your property goes after your death. If you die and you have not made a will, or if your will is invalid for any reason, then you end up being treated under the rules of Intestacy.
The rules of Intestacy are quite simple. There is a list laid down by law of people who inherit your property. This list may or may not bear any relation to the people who would have inherited your property if you had got round to making a will. But since you did not get round to making a will, in a sense it's your own fault because you had the chance and you didn't.
The really bad news is that in a really bad case you might find that all your money ends up going to the government, because if you die without leaving a will and they can't find a blood relation the government cops the lot. If that isn't a very good reason for making a will I don't know what is.
A lawyer will help you make a will to avoid these Intestacy rules, or if you have a loved one who has died without making a will then a lawyer will help take you through the system so that everything is correctly accounted for and gets to its correct destination.