Nouns:
* Hair
* Hand
* Head
* Heart
* House
* History
* Hospital
* Horse
* Human
* Hero
* Helicopter
* Hammer
* Hat
* Hope
* Honey
* Highland
* Highway
* Harbor
* Home
* Health
Pronouns:
* He
* Her
* Him
* His
* Hers
* Himself
* Herself
These are just a few examples. There are many other nouns and pronouns that start with the letter 'h'.