for

The for statement is used to repeat a block of statements enclosed in curly braces. An increment counter is usually used to increment and terminate the loop. The for statement is useful for any repetitive operation, and is often used in combination with arrays to operate on collections of data/pins.

There are three parts to the for loop header: for(initialization; condition; increment). The initialization happens first and exactly once. Each time through the loop, the condition is tested; if it's true, the statement block, and the increment is executed, then the condition is tested again. When the condition becomes false, the loop ends.
// Fade a LED brightness from zero to max
int PWMpin = 10;

void setup() {
  // no setup needed
}

void loop() {
   for (int i = 0; i <= 255; i++) {
      analogWrite(PWMpin, i);
      delay(10);
   } 
}

The C for loop is much more flexible than for loops found in some other computer languages, including BASIC. Any or all of the three header elements may be omitted, although the semicolons are required. Also the statements for initialization, condition, and increment can be any valid C statements with unrelated variables, and use any C datatypes including floats. These types of unusual for statements may provide solutions to some rare programming problems. For example, using a multiplication in the increment line will generate a logarithmic progression: The following code generates: 2, 3, 4, 6, 9, 13, 19, 28, 42, 63, 94
for(int x = 2; x < 100; x = x * 1.5){
    Serial.println(x);
}

Another example, fade a LED up and down with one for loop:
void loop() {
   int x = 1;
   for (int i = 0; i > -1; i = i + x) {
      analogWrite(PWMpin, i);
      if (i == 255) x = -1;             // switch direction at peak
      delay(10);
   } 
}