An heir presumptive is the person entitled to inherit a throne, peerage, or other hereditary honour, but whose position can be displaced by the birth of an Heir apparent or of a new heir presumptive with a better claim to the position in question.
Depending on the rules of the monarchy, the heir presumptive might be the daughter of a monarch if males take priority over females and the monarch has no sons, or the senior member of a collateral line if the monarch is childless or the monarch's children cannot inherit, either because they are daughters and females are completely barred from inheriting, because the monarch's children are illegitimate, or because of some other legal disqualification such as being born from the monarch's morganatic marriage or conversion away from a religion the monarch is required to profess.
In either case, the subsequent birth of a legitimate child to the monarch may displace the former heir presumptive by a new heir apparent or heir presumptive. It is not assumed that the monarch and his or her consort are incapable of having further children; the day before Queen Elizabeth II ascended the throne, her father, George VI, was gravely ill and her mother was in her early 50s, but Elizabeth was still considered the heir presumptive rather than the heir apparent.
Heir presumptive, like heir apparent, is not a title or position per se. Rather, it is a general term for a person who holds a certain place in the order of succession. In some monarchies, the heir apparent bears, ipso facto, a specific title and rank, this also sometimes being the case for noble titleholders, but the heir presumptive does not bear that title. In other monarchies, the first in line to the throne bears a specific title by right, regardless of whether she or he is heir apparent or heir presumptive.