I need some help understanding enum.

Yes, the instance of ordetItem at the end appears to be misspelled and should be orderItem like the first one. To understand what each instance of the orderItem name means, let's break down how typedefs and enums work in C

typedef

The typedef keyword basically tells the compiler that you're gonna use a different name for a specific type. For example, if I wanted to use the keyword number to say int, I could write this line:

typedef int number;

Later on, if I wrote the following code, the compiler would understand that when I write number, I really mean int, and everything will work just fine:

number one = 1;
number two = 2;

printf("%d", one + two);

To give a type a different name like this with typedef, you first write the type name that the compiler already knows about, then you write the name that you want to use instead

enum

You can totally declare an enum on its own without using a typedef. You would do so basically as you're doing in your question above, but without the typedef syntax, like this:

enum orderItem{
    Bucket = 1,
    Sandwich = 2,
    Soda = 3, 
    FamilyDeal = 4,
    DoubleTrouble = 5,
    LonelyBird = 6
};

However, if we wanted to declare a variable that would hold one of these values, we would still have to use the enum keyword when we declare that variable. For example, something like this:

enum orderItem meal = FamilyDeal;

That line declares a new variable called meal that holds one of the values of our orderItem enumeration. Since you already know that orderItem is an enum, it looks a bit clunky that you have to write enum all over again when you use one of the values, right?

Combined

In the code posted in your question, typedef and enum are working in concert. It's basically telling the compiler that you want an enum called orderItem, but instead of having to write enum orderItem when you use one of its values, you just want to write orderItem instead, like this:

typedef enum orderItem{
    Bucket = 1,
    Sandwich = 2,
    Soda = 3, 
    FamilyDeal = 4,
    DoubleTrouble = 5,
    LonelyBird = 6
} orderItem;

orderItem meal = FamilyDeal;

So, going through it bit by bit, the typedef keyword tells the compiler that you're going to refer to a type by a new name, the enum keyword makes a new enumeration that also happens to be the old type that the compiler already knows, the first orderItem is the compiler's name for your new enum, then comes all the possible values, and then the 2nd orderItem (or ordetItem in your original question) is the name that you want to use to refer to the previously-known type (your new enum).

The line afterwards declares a new variable called meal that holds a value from your orderItem enumeration using the name defined by the typedef, and gives it a value of FamilyDeal