From The Thought Company. We have reposted a portion of their eighteen part article below.
HOW THE SIZE OF AN ART PAINT BRUSH IS INDICATED
Artist's paint brushes come in an array of sizes, shapes and hairs. The size of a brush is indicated by a number printed on the handle. Brushes start from 000, then 00, 0, 1, 2, and up. The higher the number, the bigger or wider the brush.
Unfortunately, there is little consistency between brush manufacturers as to what these sizes actually are, so a number 10 in one brand can be a different size to a number 10 in another brand.
RELATIVE SIZES OF BRUSHES
Believe it or not, both brushes in the photo are size no. 10. Admittedly, the difference in size isn't usually so extreme; these two brushes were chosen specifically to illustrate the point.
If you're buying brushes from a catalog or online and it's a brand you're not familiar with, check to see if there's an indication of the actual width of the brushes in inches or millimeters. Don't just go by the brush size number.
THICKNESS OF A BRUSH
Not only do different brands of art paint brush vary in size even when they're supposedly the same (as indicated by the number), but also in thickness. If you're buying brushes from a catalog or online, remember to consider this if you're not familiar with a particular brand of brush.
If you're painting with watercolor or very fluid paint, a thick brush will hold considerably more paint. This enables you to paint for longer without stopping. But if you want a brush for dry-brush techniques, you may well want a brush that holds less paint.
Want to read more about Brush Shapes here is the full article describing these different brush shapes: waterbrush, fan, flat, mop, sword, rigger, and round.