The chainset as it's often referred to is the part of the bike where the pedals screw into. It can also be called the crankset. Chainsets are available in different lengths, varying quantities of chain rings and have different numbers and teeth sizes on those chain rings.
Mountain bikes historically came with a triple chainset which means they have 3 chain rings at the front to allow a wide range of gears for adverse mountain biking type terrain. With the advent of wider ratio cassettes, the need to have so many chain rings has diminished and now most mountain bikes come with 2 chain rings and some even come with just 1! chain rings are often made from a very high grade of alloy to cope with the wear from having an often dirty chain running on them. cranks can be made from a variety of materials but the most popular by far is Alloy. Carbon fibre is common at the high end but the price can be prohibitive for some people. The most common crank Arm lengths for mountain bikes are 170mm and 175mm.
Chainsets on road bikes are not dissimilar in principle to mountain bikes but they generally come with 2 chain rings and the ratios are most often 50/34 unless you are buying a race specific bike which will be equipped with a 53/39 gear ratio allowing for faster speeds to be reached. Road bikes sometimes come with a triple chainset fitted but it is very rare these days due to the wide ratio cassettes most manufacturers fit. As with mountain bikes crank arms on road bikes can be made from a variety of materials, at the low to mid end aluminium is very popular but you do get carbon fibre appearing at much lower prices on road bikes than on mountain bikes. You can also interchange the chain rings on certain chainsets in order to adjust gear ratios. The most common crank Arm lengths for road bikes are 170mm, 172.5mm and 175mm.