what does typedef struct node *NODE indicate?

Question

struct node
{
    int coef;

    int exp;

    struct node *link;
};

typedef struct node *NODE;

Answer 1

NODE becomes an alias for struct node*.

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EDIT: Okay, for the comment (if I write my answer as comment, it would be too long and not formatted):

There's no different way to write this. Here, typedef is used just to create a synonym/alias for pointer to struct node.
An example for usage would be:

void f()
{
    // some code
    NODE p = NULL;
    // do something with p
    // for example use malloc and so on
    // like: p = malloc( sizeof( struct node ) );
    // and access like: p->coef = ..; p->expr = ..
    // do something with p and free the memory later (if malloc is used)
}

is the same as

void f()
{
    // some code
    struct node* p = NULL;
    // do something with p
}

Using NODE makes it just shorter (anyway, I wouldn't advise such typedef, as you're hiding, that it's a pointer, not a struct or other type, as mentioned in @Matteo Italia's answer).

---

The format, you're referring: "typedef struct{}type_name format" is something else. It's kind of a trick in C, to avoid writing struct keyword (as it's obligatory in C, and NOT in C++). So

typedef struct node
{
    //..
} NODE;

would make NODE alias for struct node. So, the same example as above:

void f()
{
    // some code
    NODE p;
    // do something with p
    // note that now p is automatically allocated, it's real struct
    // not a pointer. So you can access its members like:
    // p.coef or p.expr, etc.
}

is the same as

void f()
{
    // some code
    struct node p;
    // do something with p
}

NOTE that now, p is NOT a pointer, it's struct node.