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.
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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.