Seedless grapes are a special bunch.
All plants -including grapes - grow from seeds. But some people prefer to munch on sweet, juicy grapes without biting on seeds too. So, grape breeders (those are people who develop different kinds of grapes) use their plant smarts to grow the seedless varieties.
Grape breeders create new seedless plants by placing the pollen of a seedless grape onto the flowers of a grape variety that has seeds. They then cut open and inspect the fruit of every single plant that grows from this match. The breeders are looking for seeds -- some plants will have seeds in their fruit and others won't.
When they find a plant that has no seeds, or maybe just has very tiny traces of seeds that you wouldn't be able to taste, the grape breeders use it to make more seedless plants. One way is to cut off small pieces of the seedless plant's vine and place it in special growing conditions in a greenhouse. Eventually, the pieces of vine will grow roots and become new, individual plants. This technique is called propagation.
Or, the breeders can graft, or attach, a piece of the seedless grape variety onto a healthy vine base, called a rootstock. Think of it like this: When someone cuts their hand, a doctor sews the cut together, and the two pieces heal as one. The grafted vines grow together the same way. And, the grape variety attached to the rootstock keeps producing delicious seedless grapes.