Clearly, you mustn’t put anything into your compost bin that
is toxic or poisonous in any way – so no harmful chemicals, cleaning products,
food that has been contaminated etc. You also mustn’t put in anything that
doesn’t rot down – eg plastic, glass, anything that would just stay in the
compost and not decompose.
As for ‘natural’ materials, most things are OK but there
are some exceptions. Any kind of solid waste product, such as cat or dog droppings, must never go in the compost, and all kinds of meat products are bad too - they either don't degrade properly or can prevent other materials from doing so, besides often attracting flies etc.
Anything coal based such as ashes, or anything with a high alkaline content such as lime should also be avoided. There are also other things that shouldn't be composted such as coloured paper, but the above will give you a general idea. You can find a detailed list of things to avoid here.