A seat post on a bike can come in a huge range of diameters ranging from 25.4mm to 35mm and sometimes above. As frame manufacturing developed with different materials so too did the diameter of the tubing. For a long time 27.2mm was classed as standard as most frames were made from steel or Cromoly. As alloy frames started to appear through new ranges from all brands the diameter became larger due to the necessity to use larger tubes on an alloy frame. The most common sizes for alloy frames are 30.9mm and 31.6mm although there are many other sizes that are used.
As carbon frame manufacturing took off, more sizes were required for different brands.
If you remove your seat post it should have the size etched or printed on it at the bottom.
As with all bike parts you can spend a little or a lot on them. The seat post is no different. Steel seat posts are usually the cheapest but they aren't made in many sizes so an alloy seat post is usually the way to go. These range from around £10 and can reach prices over £100. At the higher end the seat post are incredibly light and are often anodized.
Carbon seat posts are also available in many sizes and can offer a bit of comfort or compliance due to the materials ability to flex. Of course they are very light too so many high end brands use these to help keep the bike weight low.