>what does the "i" stand for??

It is an index into the array.

Rather than "removing all spaces" -- because you might also want to remove punctuation or control characters -- aren't you really trying to keep only letters?
Code:
#include <stdio.h>
#include <ctype.h>

int main(void)
{
   char sentence[40] = "Damn, I Agassi.\tMiss again mad.";
   int i, j = 0;

   printf("sentence = \"%s\"\n", sentence);
   for ( i = 0; sentence[i] != '\0'; ++i )
   {
      if ( isalpha(sentence[i]) )
      {
         sentence[j++] = tolower(sentence[i]);
      }
   }
   sentence[j] = '\0';
   printf("sentence = \"%s\"\n", sentence);

   for ( i = 0, --j; i < j; ++i, --j )
   {
      if ( sentence[i] != sentence[j] )
      {
         puts("Not a palindrome");
         return 0;
      }
   }
   puts("Looks like a palindrome to me");
   return 0;
}

/* my output
sentence = "Damn, I Agassi.	Miss again mad."
sentence = "damniagassimissagainmad"
Looks like a palindrome to me
*/