Pulleys aresimilar to levers. Each allows a force to be magnified to a point many times over so that an object can be moved or a force overcome. Pulleys are especially useful for lifting objects vertically. It is important to realise that, ignoring friction, that tension is the same at each point in a rope, so that if you pull the end of the rope bottom left with a force T, the weight will experience a force 3T and will rise as long as T>W/3.
Similarly the weight in the centre experiences a force 3T upwards and will rise as long as T>W/3. The weight at the right hand side experiences an upwards force of 4T and will rise as long as T>W/4. In general you can reduce the force required to lift a weight by adding more pulleys. Adding another pulley at the bottom results in an extra force T acting upwards and this reduces the force required to lift the weight W.
Since Work=Force times Distance, moving a weight by applying a smaller force means you must pull the string further. If you raise the weight by a height h, each string attached to the bottom pulley must shorten by h so you must apply the force over a distance 3h.