Heraldry, just as genealogy, has a set of terms that will help you to identify the particular parts of it and to determine where it fits into the family tree.
Some of the terms that you will come across in your genealogy research, as it pertains to and touches on heraldry will be:

Marshalling: Which was the term used when a marriage took place. It was the practice of the day to combine the coats of arms of the two families who had intermarried. Technically marshalling is arranging two more more coats of arms on one shield which tells of the family’s allies.
Some types of marshalling included impaling, which is the art of placing the arms of the husband and his new wife side by side on the shield, or escutcheon, placing the arms of the father of the bride inside a small shield which was then placed in the center of the husbands shield.

Quartering was another method used to show family lines. The children used this method more commonly, to show their family allegiance. The fathers arms are in the first quarter, and the fourth quarter, while the arms of the mothers family reside in the second and third quarters of the shield.

Cadency, which is another term that you may come across, meant that the son in each generation could use the shield of their father, but in most cases, changed it slightly, to add some small detail that would show that this was the shield of their own branch of this particular family.
The eldest son, who actually inherits the coat of arms, does also use this tradition of cadency, but on the death of his father, the paternal coat of arms reverts back to the original, and becomes his inherited right.

Females Inheriting: there have always been incidence of women who could inherit a coat of arms and to use them, however they can not pass them along to their children unless there are no brothers. If this is the case, they own the coat of arms, to pass along to their children, and are considered heraldic heiress to the coat of arms.

A coat of arms is granted by the king of arms in England, and in Ireland, while the court of the Lord Lyon King of arms grants that right in Scotland.
A repository called the College of Arms holds an official register of all granted coats of arms that exist in England and Wales. The wearing of the coat of arms is restricted. Other countries do record and permit coats of arms, but do not restrict their use.

If you have traced a persons lineage in your genealogy research to 15th or 16th century England or Wales, or some other country that grants a coat of arms, there is a chance that you can find and prove their right to use it by your genealogy skills. The next step would be to find that coat of arms in the College of Arms, and to apply for permission for its use.
For your information, here is a link to recently granted coats of arms in the countries of England and Wales.

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