This article deals around the set-up of a (extremely) low cost water filtration system. Water filtration can be used if there are few or no other options of obtaining (pure) water from other sources: ie rainwater, groundwater (rather than surface water), ... If no filtering needs to be done at all on water, it is generally cheaper, and it also avoids the use of energy (and possible air pollution). Things will depend on the local context (water source availability) however.
Purpose
The purpose of setting up the explained low-cost sytem of the water filtration is to make water clean of debris/particles aswell as the worst filth. If the water is intented to be drunk, HEAT the water to a boil (100°C) for 5 minutes (7 minutes when at a high altitude)[1]. Otherwise, you can use the water as is (ie for aquaculture, ...)
Set up
Regarding the components of the filter: it consists of grass, sand and charcoal. The first element (grass) filters out any large debris/particles. The sand also acts as a filter/sieve, pretty much in the same way as the grass. Note that I'm guessing that the grass was taken as a primary filter since this is easier to come by/cheaper than sand and thus can be replaced more often. The charcoal finally is a third filter and is the most efficient filter, it can filter out the smallest of particles, including organic organisms (ie bacteria, ...)
http://en.wikipedia.org/wiki/Carbon_filtering http://en.wikipedia.org/wiki/Sand_filter
The image of the DIY filter water filter was taken from a book about survival skills; it could be used in a rural context, ie especially in very poor areas, without much access to any building materials. However, systems set up especially for general (domestic) use may be better (water would be even more pure), and may be more sustainable and easy to maintain. For the latter type, I refer you to http://en.wikipedia.org/wiki/Treatment_pond and http://en.wikipedia.org/wiki/Rainwater_harvesting (the latter is about rainwater harvesting, but it contains some systems/information on the general set-up of domestic water filtering aswell)