The sign bit of an integer is bit 15 (counting 0..15 = 16 bits). If you want to test if this bit is set one could do so in the following way:
int nr = -25;
if ((nr & bit(15)) == bit(15)) Serial.println("negative");
Another purpose is if one reads from a register e.g. a thermometer with an alarmflag at bit pos 4
byte b = ReadRegisterFromThermometer();
if (b & bit(4) == bit(4)) // then alarm !
A more complex example is if one writes to a rigister where every bit has a different meaning.
byte b = bit(7) | bit(3) | bit(1) | bit(0); // the or operation will merge the bits set.
WriteRegister(b);
Often the code is written without the bit() function with hexadecimal values directly as follows:
if ((nr & 0x80) == 0x80) Serial.println("negative");