The NULL-termination is what differentiates a char array from a string (a NULL-terminated char-array) in C. Most string-manipulating functions relies on NULL to know when the string is finished (and its job is done), and won't work with simple char-array (eg. they'll keep on working past the boundaries of the array, and continue until it finds a NULL somewhere in memory - often corrupting memory as it goes).
In C, 0 (the integer value) is considered boolean FALSE - all other values are considered TRUE. if, for and while uses 0 (FALSE) or non-zero (TRUE) to determent how to branch or if to loop. char is an integer type, an the NULL-character (\0) is actually and simply a char with the decimal integer value 0 - ie. FALSE. This make it very simple to make functions for things like manipulating or copying strings, as they can safely loop as long as the character it's working on is non-zero (ie. TRUE) and stop when it encounters the NULL-character (ie. FALSE) - as this signifies the end of the string. It makes very simple loops, since we don't have to compare, we just need to know if it's 0 (FALSE) or not (TRUE).
Example:
char source[]="Test"; // Actually: T e s t \0 ('\0' is the NULL-character)
char dest[8];
int i=0;
char curr;
do {
curr = source[i];
dest[i] = curr;
i++;
} while(curr); //Will loop as long as condition is TRUE, ie. non-zero, all chars but NULL.
char str[5] = {'A','N','S','\0'};
andchar str1[5] = "ANS";
(if even the explicit lengths) – Brasherstr1[5]="ANS"
because the compiler puts it there for you. The string constant "ANS" allocates 4 bytes, and puts a zero terminator in the last one. – Stygian