Parole is what you say with voice. "La parole" is the ability to talk. Une parole is something you said with voice, nothing less, nothing more.
Now indeed, there are many expressions with paroles, like "prendre la parole" (to talk in a group), or "dire des paroles en l'air" (to say things you don't believe in or to say you will do something but you know you won't etc.) or "donner sa parole" (to promise, to give your word).
It's not really a question of being abstract or concrete, because the "paroles" are made of words, and actually, some expressions with "mot" mean "parole" : "ne jamais dire un mot plus haut que l'autre" (to never yell at someone), "toujours avoir le mot pour rire" (to always tell something funny), "avoir son mot à dire" (to have something to say about something), "ne pas dire un mot" (to stay quiet).