Cats purr with their throats.
Your throat's gotten slimmer lately, hasn't it?
I have a sore throat. Can you sing on my behalf?
The kanji and the word are exactly the same. That means they share meanings as well.
Since this word is made up of a single kanji (and is a body part) it uses the kun'yomi reading. You did not learn this reading, so here's a mnemonic to help you:
Remember the mnemonic from when you first learned this kanji? Well こういち is still in your throat and he doesn't want to get out. In fact, every time you tug on him, he shouts, "No Do- (のど)" but you gag and can't hear the rest. People around you think you're saying "No Do-" but it's really just the weirdo living in your throat now. What a pain...