A parasite by definition is a living organism that lives at the expense of another organism (the host). This could help to answer your question.
Parasites can have a sexual or asexual reproduction (or both of them). So we have two types of hosts:
Intermediate host: It helps parasites to grow in number and have an asexual reproduction.
Definitive host: It helps parasites to fertilize (having sexual reproduction).
Let's take the example of Plasmodium (responsible for malaria), the definitive host (the anophele) contributes to transmitting the parasite to the human. without it, the Plasmodium cannot be transmitted to humans (intermediate host) to reproduce. And without humans, it cannot reproduce too, because this is where the parasite takes its resources (from red blood cells).
So, we can see that hosts have a major role in parasites reproduction.