All rockets generate thrust by igniting an mixture of fuel and 'oxidiser'.
Liquid fuel rockets hold these two components in separate tanks, only allowing them to mix together in the combustion chamber at the base of the rocket. Liquid fuels are often difficult to handle, because the best fuels, liquid liquid hydrogen, and oxidants like liquid oxygen, need to be kept at very low temperatures to stop them boiling into gas. Solid fuel rockets, on the other hand, do not have this problem. They use different chemical fuels and oxidisers, which are mixed together from powder with a rubbery 'binding agent, to form cylinder-shaped 'fuel grains'. Solid fuel is much easier to handle than liquid, and so is also cheaper.