Grandparents are the father or mother of a person's own father or mother, being respectively a grandfather (also colloquially grandpa, grandad, gramps, or many other terms) and a grandmother (also grandma, granny, grandmama, or many other terms). Everyone has a maximum of four genetic grandparents, eight genetic great-grandparents, sixteen genetic great-great-grandparents, etc. Sometimes these numbers are lower and in the case of having only two or three grandparents sibling or half-sibling incest would be involved.
In cases where the parents are unwilling or unable to provide adequate care for their children, grandparents often take on the role of primary caregivers.
One can also be a step-grandparent. A step-grandparent can be your parent's stepparent or your stepparent's parent. A stepparent's stepparent is called a step-step-grandparent, etc.
The various words for grandparents at times may also be used to refer to any elderly person, especially the terms gramps, granny, grandfather, and grandmother.
Also note that two individuals who share the same grandparents but are not siblings are called first cousins because your grandparents are also the parents of your aunts or uncles who are the siblings of your parents and the relation between your grandparents uncles aunts and first cousins is the same as your relation to your grandparents and parents.
When used as a noun (i.e., "…a grandparent walked by"), grandfather and grandmother are usually used, although grandpa/grandma and granny are often used. When preceded by "my…" (i.e., "…my grandpa walked by"), all forms are common (anywhere from "…my grandfather…" to "…my gramps…"). All forms can be used in plural, but gramps (plural gramps) is rare.
In writing, grandfather and grandmother are most common. In speech, grandpa and grandma are most common in the US, where grandfather/-mother is very rare when referring to a grandparent in person. In Britain and New England nan, nana, nanny and other variations are often used for grandmother in both writing and speech.
Numerous other variants exist, such as gramp and grandpap for grandfather and grandmom, grandmama and grammy for grandmother, etc. Because of the terms' unavoidable familiarity, there are many simplified versions as well, including grampy, granddaddy, grandpappy, etc.
Given that people may have two living sets of grandparents, some confusion arises from calling two people "grandpa" or "grandma", so often two of the other terms listed above are used for one set of grandparents. Another common solution is to call grandparents by their first names ("Grandpa George", "Grandma Anne", etc.) or by their family names ("Grandpa Jones", "Grandma Smith"). In America (where most families are of mixed ethnicity), many families call one set of grandparents by their ethnic names (i.e., Hispanic grandparents might be called "Abuelo" and "Abuela", French grandparents might be called "Pépère" and "Mémère", or Dutch and German grandparents might be called "Opa" and "Oma").