LCD = Liquid Crystal Display. Each tiny segment of an LCD screen is made of a special material that becomes more or less transparent according to the current passing through it. (Although we often say "LCD display", actually it's incorrect because the D already stands for 'display').
TFT = Thin Film Transistor. An advanced form of LCD in which each segment of the display is driven by its own transistor that's embedded in the display plate itself. The transistors are made with a process called thin-film technology. Each transistor is very small and very thin. A high-resolution LCD monitor has to have many, many transistors.
TFT is used for practically all modern complex LCDs, but simpler displays with only a few segments use non-TFT structure. That is, the transistors are separate from the display plate, usually included in a special driver IC (Integrated Circuit).