TFT is backlit, so you have a light that shines through crystals, the crystals change the colour of the light to give you red, green and blue. If they are all blocked (no red, green or blue) then you get black. However the backlight is still on and you will never get 100% black.
OLED (all mobiles will be AMOLED as a passive matrix would use too much power), is where individual LEDs (Red Green & Blue) are lit, there is no backlight and to create black they simply all switch off giving a 100% true black.
OLED contrast ratio is hugely superior to any LCD.
Obviously OLED only uses power when creating a non black so as a result it uses less power.