Transreflective LCDs reflect ambient light to illuminate the display, like classic Casio LCD wristwatches. The backlight is only needed to illuminate the display in the dark.
Transmissive LCDs require the backlight to be on for the characters to be visible, as no ambient light is used to illuminate the display. This also means if ambient light is bright (full sunlight), the characters will be difficult to see.
Positive versus negative refers to whether the the dots to create the characters are on and the background is off (STN+) or the character pixels are off and the background is on (STN-).