Let's start with what a paint by number is. A paint by number is a guided painting experience. Paint by numbers are "kits" that come with everything you need to finish a painting. A classic paint by number might be of a lighthouse, a cat, or of some fall tree foliage. A typical kit will have a canvas, paints, brushes, and some instructions.
The canvas will have some printed borders dividing the canvas into hundreds or thousands of regions. Each of those regions will have a number. These numbers will correspond to the numbers on the unique individually wrapped paints. Commonly there will be 20-36 paints. The painter then uses the brushes to apply the paint to the matching regions on the canvas. If the painter does a reasonably good job of this, they will produce the painting.
A "custom" paint by number adds an extra dimension. Instead of the manufacturer choosing a few images and mass producing a bunch of paint by number kits of each image, instead the customer chooses a personal or treasured photo to have transformed into a paint by number. If you'd like to order a custom paint by number, you can go here to get started.