True only if both operands are true, e.g.

if (digitalRead(2) == HIGH  && digitalRead(3) == HIGH) { // read two switches 
  // ...
} 

is true only if both inputs are high.

True if either operand is true, e.g.

if (x > 0 || y > 0) {
  // ...
} 

is true if either x or y is greater than 0.

True if the operand is false, e.g.

if (!x) { 
  // ...
} 

is true if x is false (i.e. if x equals 0).

Make sure you don't mistake the boolean AND operator, && (double ampersand) for the bitwise AND operator & (single ampersand). They are entirely different beasts.

Similarly, do not confuse the boolean || (double pipe) operator with the bitwise OR operator | (single pipe).

The bitwise not ~ (tilde) looks much different than the boolean not ! (exclamation point or “bang” as the programmers say) but you still have to be sure which one you want where.

if (a >= 10 && a <= 20){}   // true if a is between 10 and 20

* & (bitwise AND) * | (bitwise OR) * ~ (bitwise NOT * if (conditional) and ==, !=, <, > (comparison operators)

Source: arduino.cc