The verbs dejar, parar and terminar form constructions with the infinitive. Compare:
El niño ha parado de comer = The child was eating, and then he stopped. Maybe then he'll keep eating
El niño ha dejado de comer = The child used to eat normally, but lately he's had little appetite
El niño ha terminado de comer = The child is no longer eating because he has eaten everything, he has finished his dish
How can we understand it?
When an action ends but then it can start again, we use the construction parar de + infinitivo:
Ha parado de llover = It was raining and now it's not. But maybe it's going to rain again
Juan ha parado de estudiar = Juan has made a pause and then he's going to continue
When we no longer carry out a continuous action because we have decided so, we use the construction dejar de + infinitivo:
He dejado de fumar = He used to smoke but he no longer smokes because it's his decision
Juan ha dejado de estudiar = Juan has abandoned his studies
The construction terminar de + infinitivo means to complete an activity:
Juan ha terminado de estudiar a las 7 = Juan finished his assignment at 7, he's done everything he was supposed to do
Juan ha terminado de estudiar = Juan has completed his University degree
Looks simple, right? Now let's look at four special uses of these constructions.
We often use para de + infinitivo to ask someone to finish an annoying action:
¡Para de molestarme! ¡Para ya! = Don't bother me again!
The negative construction no parar de + infinitivo conveys the idea of an action that never ends, always repeating itself:
No para de llover = It rains and rains and rains...
For delicate requests and suggestions no dejes de + infinitivo is used a lot, which equals to "I encourage you to do something":
No dejes de soñar = Dare to dream, I advise you to continue dreaming
No dejes de llamarme si tienes dudas = You can call me if you have doubts, I encourage you to call me
Finally, no terminar de + infinitivo equals to not being able to perform an action no matter how hard you try:
No termino de comprenderlo = I'm trying to understand it, but I can't
Mi madre quiere comprarse un coche, pero no termina de decidirse = It is very difficult for my mother to choose a suitable car