When printf() is called with %s it will more or less do the following

for(i = 0; pointer[i] != '\0'; i++)
{
   printf("%c", pointer[i]);
}

What you want do is something like

for(i = 0; pointer[i] != '\0'; i++)
{
   printf("\n Element is %c", pointer[i]);
}

When you are referencing specific elements in an array you must use a pointer AND an index i.e. pointer[0] in this case 0 is the index and 'pointer' is the pointer. The above for loops will move through the entire array one index at a time because 'i' is the index and 'i' increases at the end of every rotation of loop and the loop will continue to rotate until it reaches the terminating NULL character in the array.

So you might want to try something along the lines of this.

void printoutarray(char *pointertoarray)
{
  for(i = 0; i <= 2; i++)
  {
    printf("\n Element is: %s \n", pointertoarray[i]);
  }
}

int a, b;
char answer[20][256];//<- array of char[256]

for(a=0; a<20; a++)//<- 0 origin
{
    scanf("%255s", answer[a]);//<- Reading of the string with a maximum 255 characters (One is reserved for the termination character('\0'))
}

for(b=0; b<20; b++)
{
    printf("%s\n", answer[b]);
}

Given that the code is really simple, I see mostly coding style issues with it.

Instead of this:

char *names[] = {
    "John", "Mona",
    "Lisa", "Frank"
};

I would prefer either of these writing styles:

char *names[] = { "John", "Mona", "Lisa", "Frank" };

// or

char *names[] = {
    "John",
    "Mona",
    "Lisa",
    "Frank"
};

The pNames variable is pointless. You could just use names.

Instead of the while loop, a for loop would be more natural.

This maybe a matter of taste, but I don't think the Hungarian notation like *pArr is great. And in any case you are using this pointer to step over character by character, so "Arr" is hardly a good name. I'd for go for pos instead. Or even just p.

You should declare variables in the smallest scope where they are used. For example *pos would be best declared inside the for loop. In C99 and above, the loop variable can be declared directly in the for statement.

The last return statement is unnecessary. The compiler will insert it automatically and make the main method return with 0 (= success).

Putting it together:

int main(int argc, char *argv[])
{
    char *names[] = { "John", "Mona", "Lisa", "Frank" };
    for (int i = 0; i < 4; ++i) {
        char *pos = names[i];
        while (*pos != '\0') {
            printf("%c\n", *(pos++));
        }
        printf("\n");
    }
} 

Actually it would be more interesting to use argc and argv for something:

int main(int argc, char *argv[])
{
    for (int i = 1; i < argc; ++i) {
        char *pos = argv[i];
        while (*pos != '\0') {
            printf("%c\n", *(pos++));
        }
        printf("\n");
    }
} 

The straight forward approach is simply:

#include <ansi_c.h>//collection of all ansi C headers files in my environment.  
                   //replace this with appropriate headers supporting your environment
int main()
#define MAX_DIGIT_LEN 10 //memory allocation for char *b

{
   int a[5] ={1,2,3,4,5};
   int i ; 
   char *b; //in your original post, you never set 
            //this pointer to point to any space
            //it was therefore an uninitialized 
            //pointer, with no memory space.  

   //you must initialize pointers, and allocate some memory.
   //Somthing like this will work:   

   //memory must be MAX_DIGIT_LEN * number of ints in array 
   b = malloc(MAX_DIGIT_LEN*(sizeof(a)/sizeof(a[0]))+1);//using "sizeof(a)/sizeof(a[0]" 
                                        //will accommodate array size changes 
                                        //+1 allows for NULL byte at end of char array
   sprintf(b, "%d%d%d%d%d", a[0],a[1],a[2],a[3],a[4]);    
   printf("\n %s",b);
   free(b);

   return 0;
}  

Produces this output:

If you want to use a loop, then consider using (creating) an additional variable:

#include <ansi_c.h>//collection of all ansi C headers files in my environment.  
                   //replace this with appropriate headers supporting your environment

#define MAX_DIGIT_LEN 10 //memory allocation for char *b
int main()  
{
   int a[5] ={1,2,3,4,5};
   int i ; 
   char *b;
   char buf[MAX_DIGIT_LEN];
               //create this as an intermediary place 
               //to store discrete elements of a[]
               //arbitrarily chose 10, to hold up to 
               //9 digit integer, such as 123456789.
               //if you anticipate larger digits, 
               //use a bigger index to create buf[] 

   //memory must be MAX_DIGIT_LEN * number of ints in array 
   b = calloc(MAX_DIGIT_LEN*(sizeof(a)/sizeof(a[0]))+1, 1);
                                           //note calloc (rather than malloc) is 
                                           //preferable here to initialize
                                           //all memory space with 0 before
                                           //attempting strcat() calls.

   for(i=0 ; i<sizeof(a)/sizeof(a[0]) ; i++)
   {   
       sprintf(buf, "%d", a[i]);
       strcat(b,buf);
   }      
   printf("\n %s",b);
   free(b);

   return 0;
}  

Produces this output: