The informal French expression casser les pieds à quelqu’un has two different meanings. It can mean to bore someone stiff, or it can mean to annoy someone, to get on their nerves.
While it is annoying to be bored stiff, neither meaning seems to have much of anything to do with broken feet - except, if you stretch it a little, for an overwhelming desire to run away as fast as you can, or kick the annoying person so hard that you might hurt your foot. It turns out the medical condition the idiom refers to isn't as bad as broken bones. While commonly used in everyday French, it is a slightly slangy expression, so probably inappropriate for your next work presentation.
The association of the verb casser with a body part is found as early as the 12th century, when casser was understood as écraser (to crush.) The meaning was to cause pain, which was certainly very annoying. But it's only in the middle of the 15th century that the idea of actually annoying a person was added.
The body parts most often used at the time were the brain - casser la cervelle - and the ears - casser les oreilles. At the end of the 19th century, those were gradually replaced with feet, while always keeping the notion of disturbance. Note that casser les oreilles is still in use today, but mainly with the meanings of either being too loud or talking too much about something.
Nowadays, there are a number of other body parts people might be eager to crush, mostly located in the nether regions. Depending on the level of language used, the options will range from cute to truly vulgar. Increasingly, you will even hear the illusive
il me les casse - he's breaking them - where one is free to fill in the blanks. We highly recommend sticking to les pieds. The expression casser les pieds can also be turned into a noun or an adjective: un(e) casse-pieds is someone who is very annoying. Not to be confused with un casse-tête - a puzzle, a brain-teaser - or un casse-cou - a reckless person.
Ça me casse les pieds!
This is getting on my nerves!
Ce prof casse les pieds de tous ses étudiants.
That teacher bores all of his students.
Cet homme est vraiment casse-pieds avec tous ses problèmes!
This man is a real pain in the neck with all his problems!