There is no "callback" in C - not more than any other generic programming concept.

They're implemented using function pointers. Here's an example:

void populate_array(int *array, size_t arraySize, int (*getNextValue)(void))
{
    for (size_t i=0; i<arraySize; i++)
        array[i] = getNextValue();
}

int getNextRandomValue(void)
{
    return rand();
}

int main(void)
{
    int myarray[10];
    populate_array(myarray, 10, getNextRandomValue);
    ...
}

Here, the populate_array function takes a function pointer as its third parameter, and calls it to get the values to populate the array with. We've written the callback getNextRandomValue, which returns a random-ish value, and passed a pointer to it to populate_array. populate_array will call our callback function 10 times and assign the returned values to the elements in the given array.

Here is an example of callbacks in C.

Let's say you want to write some code that allows registering callbacks to be called when some event occurs.

First define the type of function used for the callback:

typedef void (*event_cb_t)(const struct event *evt, void *userdata);

Now, define a function that is used to register a callback:

int event_cb_register(event_cb_t cb, void *userdata);

This is what code would look like that registers a callback:

static void my_event_cb(const struct event *evt, void *data)
{
    /* do stuff and things with the event */
}

...
   event_cb_register(my_event_cb, &my_custom_data);
...

In the internals of the event dispatcher, the callback may be stored in a struct that looks something like this:

struct event_cb {
    event_cb_t cb;
    void *data;
};

This is what the code looks like that executes a callback.

struct event_cb *callback;

...

/* Get the event_cb that you want to execute */

callback->cb(event, callback->data);

Callbacks in C are usually implemented using function pointers and an associated data pointer. You pass your function on_event() and data pointers to a framework function watch_events() (for example). When an event happens, your function is called with your data and some event-specific data.

Callbacks are also used in GUI programming. The GTK+ tutorial has a nice section on the theory of signals and callbacks.

This wikipedia article has an example in C.

A good example is that new modules written to augment the Apache Web server register with the main apache process by passing them function pointers so those functions are called back to process web page requests.

It is lot easier to understand an idea through example. What have been told about callback function in C so far are great answers, but probably the biggest benefit of using the feature is to keep the code clean and uncluttered.

Example

The following C code implements quick sorting. The most interesting line in the code below is this one, where we can see the callback function in action:

qsort(arr,N,sizeof(int),compare_s2b);

The compare_s2b is the name of function which qsort() is using to call the function. This keeps qsort() so uncluttered (hence easier to maintain). You just call a function by name from inside another function (of course, the function prototype declaration, at the least, must precde before it can be called from another function).

The Complete Code

#include <stdio.h>
#include <stdlib.h>

int arr[]={56,90,45,1234,12,3,7,18};
//function prototype declaration 

int compare_s2b(const void *a,const void *b);

int compare_b2s(const void *a,const void *b);

//arranges the array number from the smallest to the biggest
int compare_s2b(const void* a, const void* b)
{
    const int* p=(const int*)a;
    const int* q=(const int*)b;

    return *p-*q;
}

//arranges the array number from the biggest to the smallest
int compare_b2s(const void* a, const void* b)
{
    const int* p=(const int*)a;
    const int* q=(const int*)b;

    return *q-*p;
}

int main()
{
    printf("Before sorting\n\n");

    int N=sizeof(arr)/sizeof(int);

    for(int i=0;i<N;i++)
    {
        printf("%d\t",arr[i]);
    }

    printf("\n");

    qsort(arr,N,sizeof(int),compare_s2b);

    printf("\nSorted small to big\n\n");

    for(int j=0;j<N;j++)
    {
        printf("%d\t",arr[j]);
    }

    qsort(arr,N,sizeof(int),compare_b2s);

    printf("\nSorted big to small\n\n");

    for(int j=0;j<N;j++)
    {
        printf("%d\t",arr[j]);
    }

    exit(0);
}

Usually this can be done by using a function pointer, that is a special variable that points to the memory location of a function. You can then use this to call the function with specific arguments. So there will probably be a function that sets the callback function. This will accept a function pointer and then store that address somewhere where it can be used. After that when the specified event is triggered, it will call that function.