heir: the person with the legal right to receive an inheritance
An heir is the one in line to receive what belongs to another, usually a father's estate passing to a son. The word names the person, not the property: the estate itself is a different word (κληρονομία), and the act of coming into it is another (κληρονομέω). In the parable of the vineyard the tenants recognize the owner's son as "the heir" and plot to kill him precisely so the inheritance will fall to them, which shows the plain legal force of the term: the heir is the rightful future owner.
The New Testament takes this everyday legal picture and applies it to God's people. Believers are called "heirs of God," "heirs of the promise," "heirs of the kingdom," and "heirs of eternal life," meaning they hold a secure, God-given claim to what he has promised. Paul presses the image furthest in Romans, where believers are "joint heirs with Christ" (συγκληρονόμος), sharing in what belongs to the Son.
Both uses are the same word with the same core idea: a person who will rightfully receive a possession. The only difference is whether the inheritance is a literal estate or the blessings God has pledged.