what does else if (!*p) mean in this code

I am trying to understand how this program works and i found something that i dont understand it was in this part

if (!isempty(stack) || *p) {
      puts("Invalid parenthesis expression");

      while (! isempty(stack))
        pop(&stack);
    }
    else if (!*p)
      puts("Valid parenthesis expression");

The full coding is here

#include<stdio.h>
#include<malloc.h>
#include <string.h>

typedef struct data{
  char parent;
  struct data *next;
} DATA;

void push(DATA **stack, char parentheses);
int isempty(DATA *stack);
void pop(DATA **stack);
int top(DATA *stack);

int main(int argc, char const *argv[]){
  DATA *stack = NULL;
  char parentheses[100];
  char * p;

  while (fputs("Enter parentheses: ", stdout),
         (scanf(" %99[^\n]", parentheses) == 1) && strcmp(parentheses, "-1")) {
    for (p = parentheses; *p; ++p) {
      if  ((*p == '{') || (*p == '[') || (*p == '('))
        push(&stack, *p);
      else {
        char o;

        if (*p == '}')
          o = '{';
        else if (*p == ')')
          o = '(';
        else if (*p == ']')
          o = '[';
        else
          o = 0;

        if (isempty(stack) || (top(stack) != o))
          break;

        pop(&stack);
      }
    }

    if (!isempty(stack) || *p) {
      puts("Invalid parenthesis expression");

      while (! isempty(stack))
        pop(&stack);
    }
    else if (!*p)
      puts("Valid parenthesis expression");
  }

  return 0;
}

void push(DATA **stack, char parentheses) {
    DATA *node = malloc(sizeof(DATA));

    node->parent = parentheses;
    node->next = *stack;
    *stack = node;
}

int isempty(DATA *stack) {
  return (stack == NULL);
}

void pop(DATA **stack) {
  DATA *temp = *stack;

  *stack = (*stack)->next;
  free(temp);
}

int top(DATA *stack) {
  return stack->parent;
}