Typically, plastic waste placed in your yellow topped bin is sorted and baled, then sold on to third parties.
These third parties, normally businesses, then use it for a range of things, often depending on quality and market demands. It may be reprocessed to make new products or mixed with virgin materials. Sometimes its incinerated and used as a cheap source of energy and an alternative to fossil fuels. At other times, if there is limited demand making the cost of reprocessing it to high, it may still end up in landfill. If you place plastic waste (including hard and soft plastics) in your general waste bin these will most likely end up in landfill.