To parboil is to cook by boiling (typically in a covered saucepan), but only up to the point where a vegetable, pasta, or other food is slightly crunchy. Some refer to it as “precooking”, meaning that the ingredient will be cooked again by another method, so you don’t want to boil it too long. However, I often parboil vegetables to serve them cooled or at room temperature. The parboiling takes the raw “edge” off, but leaves them tasting fresh.
When parboiling (unless you will continue cooking them soon by another method), immediately drain the vegetables in cold water to stop the cooking process as soon as they reach the desired texture. Parboiling pasta is common in recipes for lasagna or other dishes that involve baking after the pasta is cooked. Noodles are parboiled in Jewish kugel or noodle pudding too, because like lasagna, that dish is baked after the noodles are boiled.
Blanching is a broader term for pre-cooking and includes frying for a few minutes in preparation for another stage of cooking, such as deep frying. Parboiling is a type of blanching.