What Is Grafting?

Wondering what grafting is?   Here are a couple definitions from authoritative books:

In The Grafter's Handbook (3rd ed. 1968), R. J. Garner defines grafting as the "horticultural practice of uniting parts of two plants so that they grow as one".

The California Master Gardener Handbook (UC ANR Publication 3382) states that grafting is "a method of asexual plant propagation that joins plant parts so that they will grow as one plant".

To me grafting is a process that enables multiple varieties of a fruit type (and in selective cases multiple varieties of related fruit types) to grow together on a single plant.

While science plays a major role in grafting, successful grafting is largely an art requiring patience, precision, and skill (and maybe a little luck).