Grafting is taking vegatative propagation techniques in which a piece of stem or a single bud of a selected variety (scion) is fuesed with a roostock. Rootstock such as (flying Dragon, one example) is used as stock.
Grafted citrus endure cold temps better than non-grafted and are more disease resistent.
Check your citrus..near the bottom between trunk and first branches, if grafted, you'll find a line which shows where your plant was grafted. Toni

To enlarge on what Toni said -- in grafting, you are surgically attachine part of one plant (the scion) to another plant (the rootstock), so the top of the tree will be genetically different from the bottom. Rather as if in people, we could get head transplants. the scion determines the variety of fruit that will be borne by the finished tree. The rootstock determines vigor (or dwarfing), cold hardiness (in citrus only), disease resistance, etc.

To make it very broadly general, grafting is when you vegetatively fuse a clonal material (usually another cultivar, be it buds or scionwood stick) unto another plant so that the fused clonal material will grow on the stock plant.

The clonal material term is used so that you plan on letting that material with its own DNA live off the destination plant.

The clonal material could be exactly the same cultivar as the branch of the destination stock to graft to, as is common when you take material from a mature plant grafted unto the seedling of the same cultivar with the aim to speed up the blooming of the propagated plant.

The DNA may even be distantly related, it could even be non-citrus, as sometimes such things could be observed and am no longer surprised, but such phenomenon are very rare. More often, plants in the same subspecies, then genus, then family will have decreasing likelihood of success in the fusion. But again, there are rare cases where they are supposedly closely related but have very low success of taking based on my experiences.

I have 30 kinds of citrus varieties in one tree. I also have several branches where the end cultivars are various kinds of Satsumas which are grafted to a navel branch which in turn is grafted unto a Lisbon lemon and in turn was grafted unto the trifoliate rootstock, and the satsumas are vigorously growing.

That is so cool. 30 different kinds. Do you have to graft at any certain age or does it matter?

The link below shows thumbnails of my grafted citruses. Select picture 39 and would show my citrus when it has still 27 grafted cultivars. It is the one on the left, the one on the right is my grafted pigmented orange tree, it is composed of oranges that are non-colored orange flesh.

The age doesn't matter but the vigor of the branches does. I love to graft on the most vigorous branches. You graft unto it, you control the growth of the tree and keep it nicely balanced. I usually regraft the slowest cultivar unto the most vigorous branches.

All my citrus grafts have been done using T-budding and MrTexas has a nice pictorial demo on how to do it.

Here is a link that might be useful: multigrafted citrus