They re the only way to enhance link s abilities.
Swap containers botw.
You can use this.
It essentially lets you pay 20 rupees to swap a heart for a fifth of a stamina wheel and vice versa.
First off head to hateno village the nearest shrine to warp to is the myahm agana shrine which basically sits right next to the village.
The more hearts the more health link has and the more hits he can take before needing to replenish his health through various means.
With each new heart container link gets another heart added to the meter in the upper left corner of the screen.
In breath of the wild getting more heart containers is directly tied to increasing link s.