Partial correlation is a way of figuring out how two things are related to each other, while taking into account the other things that might influence them. Think of it like getting rid of all the things in the middle so you can look at the stuff that is really connected.
Imagine you want to find out how much ice cream someone eats every week and how much they weigh. You could ask a bunch of people how much ice cream they eat and how much they weigh. But you might find that the people who eat a lot of ice cream also exercise a lot and that has an effect on how much they weigh. To get rid of those other things (like how much someone exercises) that could be affecting the answer, you can use partial correlation.
Partial correlation looks at how two things are connected without looking at any of the other things that might affect them. So if we use partial correlation to look at the relationship between how much ice cream people eat and how much they weigh, we can be sure that the other things that might affect the answer (like how much exercise they do) aren't affecting the result.