"Un mot" is "A word". "La parole" is "The speech" (The words / Les mots) are made with letter(s). They can be read, and pronounced. (The speech / La parole) is the way to speak, to produce sounds and using words. The speech / La parole cannot be read. I can write this message without using my speech/ma parole (my voice), but I have to use words to be understandable. If you was in front of me, and if I was using my voice to explain the difference I would be using my speech/ma parole (my voice), and I would also be using words to be understandable. Do you see the difference now ? Sometimes "La parole" can be a synonym of "Le discours" (which is also translated as "The speech" in English). In this case it's more about "an idea", "an opinion", something symbolic. For example "the speech / le discours / la parole) of someone in a religious book, or a political party. "La parole de Dieu" "Un mot" can also be "A note" about a little piece of paper with something written on it. "Je t'ai laissé un mot sur la table" :)

I'm not a native speaker myself, but I can add that in French they also use 'parole', or rather 'paroles', in the same sense that in English they talk about a song's 'lyrics', 'les paroles d'une chanson". Bye, David.

Je t'en prie.

Great explanation ! Thanks to you @Frank, @Jojo and @David G. Je vous remercie beaucoup!

I agree with @Jojo. "Je te donne ma parole" is a way to say "I promise / I swear". And thanks to @David G ! I didn't think about that translation of "Lyrics", but yes, you're absolutely right "Les paroles d'une chanson / The lyrics of a song" :) So, as you can see, it's quite difficult to really explain the senses of "Parole" in French, because that can be related to many things. But if "La parole" looks like the verb "Parler", the relation can be the same as "La vue" and "Voire", or "La marche" and "Marcher", "Le chant" and "Chanter".