TFT stands for "thin-film transistor." LCD stands for "liquid crystal display." Both terms refer to the flat-panel display, or screen, of a computer monitor or television set.
TFT v. LCD
LCD is a generic term. A TFT display is one kind of LCD.
TFT displays are made using large sheets of transistors, each one of which is controlled independently. A TFT screen is an "active-matrix" screen where each pixel of the display is illuminated individually.
Sharpness and Speed
A TFT display is sharper and brighter than a common LCD display. It refreshes more quickly than a regular LCD display and shows motion more smoothly.
TFT displays use more electricity than regular LCD screens, so they not only cost more in the first place, but they are also more expensive to operate.
A TFT display is much higher quality than a regular LCD display. It is a better display in every way, except that it is more expensive.