Our food is the source of many compounds that are needed to keep our body working. Some of these are directly available from the food (vitamins), others (provitamins) have to be converted first in our body to their final structure before we can actually use them.
Chemically, all these compounds belong to very different classes, but we can roughly divide them into two groups by one property, their solubility in water.
The vitamins that are insoluble in water are soluble in fat.
Did you ever step into a piece of tar on the beach and the tar wouldn't get off your foot no matter how often you jumped into the sea? But with a bit of tanning oil, which is insoluble in water, it was usually no problem to remove the tar from your foot.
The same principle applies for the vitamins.
Digestion of (vegetable) oils together with food, such as carrots, helps your intestines to take up the fat-soluble provitamins and vitamins more easily.