What is the meaning of the word "nag"?

Definitions:

A horse, especially one that is too old to be useful. NOUN
- The nag on the farm didn't have many years left.
- The town is full of horses no one wants- some of them perfectly healthy, but many of them starving, broken-down nags.
Repeatedly reminding or urging someone to do something, typically in a way that is perceived as bothersome or annoying. VERB
- His mother wouldn't stop nagging about his messy room, which made him less inclined to clean it.
Someone who is always criticizing or complaining. NOUN
- He's a real nag when it comes to keeping the house tidy.
To annoy or irritate someone by persistent fault-finding, complaints, or demands. VERB
- She nagged him to take out the trash until he finally did it.
To criticize or complain often in an annoying way, especially in order to try and make someone do something. NOUN
- My mom is always nagging me to get my hair cut.