"The First Vikings" (from "Archeology" about uncovering 8th century burial boats)

[intaglio]

3. Okay

The keel has 2 functions, structural and navigational.

Structurally it serves as the backbone of the vessel from which everything else is built. It keeps the boat rigid so that it doesn't snake through the water nor does it hog or sag

source Wikimedia Commons author George William Herbert

Navigationally it increases the area resisting the sideways movements caused by wind on side or sails, because there is this resistance sailboats can use side on winds to still go forward. The more lateral resistance there is the more a sailboat can head into the wind (sail close to the wind).

Boats are actually kept upright by the shape of the hull, crudely put a plank does not float narrow side down.

On Edit: Boats are actually tipped by the action of wind on sail and water on keel.