I think that is called a hierarchical menu, but I don't think that Pop-Up Menus in Numbers support that.
One way could be to have all you food items in one column. Type them, select them all, then Format Panel > Cell > Data Format > Pop-Up Menu:
Start with Blank (it will show None) is handy if you want to cancel an entry. In the Format Panel you can drag menu items to reorder them, or double click to rename.
Another way (if you want to distiguish different food groups) is to have another column with Pop-Ups for Fruit and Meat:
Then you can sort the table by Food group or Food.
There is no good way to do hierarchical menus in Numbers. With a small list of words you can use a stepper or slider cell next to a cell that gets a word from a list based on what number is in the stepper/slider cell. In ohter words, if the stepper has a "2", the formula will get the second word from your list. The user cannot see a list of words to choose from but can step through the words until they get to the one they want. There have been posts on this over the past few years. It applied/applies to Numbers '09 also.
100 categories x 100 sub categories (sort) x 100 sub-sub categories (detail information) = 1 million cells of data to create the pop ups. Is this what you really have?