In Dark Souls, normally kindling a bonfire raises its Estus Flask allotment to a maximum of 10 uses.
A regular kindling requires the player to spend one Humanity while in human form. Once kindled, that bonfire gives 10 Estus uses whenever it is rested at, rather than the standard 5. The Rite of Kindling can raise the total further, but it is a separate upgrade obtained after defeating Pinwheel and allows a bonfire to reach 15 uses.
The Firelink Shrine bonfire is a notable exception early in the game because it begins with 10 uses. Later, the player can reach 20 uses at bonfires that receive the highest level of kindling, but that is not the result of ordinary kindling alone. This distinction explains why 10 is the correct normal maximum.