Simple answer, they're cheap! Obviously then, we're not talking about the Games Workshop stuff! I mean those figures produced by the likes of HaT, Italeri and Zvezda. That's how I was introduced to the hobby in the first place. Plastic figures and DBA rules. Using these figures, I pulled together my first wargaming armies - one 25mm (actually, they are 20mm figures on 25mm bases) DBA army of Romans and one of Ancient British. I have since been able to pull together a 400+ Army Point Early Imperial Roman DBM army for about $NZ 75, and a 450+ Ancient British army (with enough warband to make about 4 other generic 'Barbarian' armies) for about $NZ 60. Admittedly, I was lucky enough to get hold of a whole heap of Airfix Ancient British figures (including 11 chariots) for $NZ 20, but even so, if you compare the prices of plastic with 25mm metal figures, the attraction to plastic becomes obvious! They even compare favourably to 15mm, at two third's the price.
When combined with DBA and HOTT - Hordes Of The Things (the fantasy version of DBA) wargame rules, infantry armies of which can usually be made out of a single box of figures costing between $NZ 10 & $NZ 13, plastic figures make an ideal introduction to the hobby.
Your average plastic figure is better able stand up to the rigours of wargaming than their metal counterparts, such as constant handling , shipment to and from the club, and the occasional drop onto the garage floor (courtesy of the inquisitive fingers of young children). And the plastic is flexible, which means it will bend when forced to (courtesy of the above) and will pretty much always bounce back into its original shape when you let go.
Actually, that's not entirely correct. The figures are made up of polythene, but depending on the mixture the manufactures uses, the plastic will come out either soft and very pliable (with great "memory", so that it will always bounce back to its original shape), or more rigid, so that with a little force, you can bend a limb, for instance, and it will stay in the new position you have placed it.
Generally, it is possible to alter a plastic figures pose/shape with the intervention of either a little gentle force, heat (such as placing the figure in a bowl of boiling water to soften it up before bending it), or a very sharp knife.
However, there are a few things to consider when looking at plastic figures.