PLA is polylactic acid filament which is heated in a 3d printer to make the models. its comes as a plastic wire 1.73mm thick and is pushed through a nozzle as the machine traces the pattern of the model. So a 2d picture placed on top of each other to make a 3d model. Its cheap and easy to use, so a good beginner way of making 3d printed models. the downside is you get layer lines on the models, especially large flat surfaces. Its is good for large models.
Resin is a Liquid Photopolymer Resin which is cured (made hard) by UV Lights. It is toxic when in the liquid state, but harmless when cured. It is good for smaller models and where you want high detail, something you can't get with PLA. Downside is that the resin is more expensive than the PLA filament and has more clean up and curing. So the price is higher for the better quality.