Worms are gross.
There are two types of worm that can affect your pet and cause illness and death as well as in some cases be transmitted to you. These are roundworm and tapeworm. Your cat can get infected, or perhaps a better word would be infested, by other animals with worms, by eating worm larvae or by eating raw meat or other infected prey animals, so it is important to have a worm control plan with your vet, as a precaution.
The obvious signs are the worms themselves, you might see them in faeces or vomit, or hanging out of your pets bottom. Yucky! But other than actually seeing them, vomiting, diarrhoea, weight loss, dry and coarse fur, increased appetite and a bloated and distended belly are also symptoms of a worm infestation.
To explain why this is serious, worms can live in your body, burrow into your organs and cause malnutrition, diarrhoea, seizures and a whole load of complicated other issues which could leave you susceptible to infections such as Tuberculosis and Malaria. There is, kind of, no end to the damage or the disgustingness.
So people, this is important. if you see any wormy looking white things around your pet then you need to wrap them up in a bit of damp kitchen paper and take them and your cat to your vet.
At home you can reduce the risks by washing and disinfecting your cats food bowl and drinking fountain regularly, by keeping litter boxes and any housing or play areas clean and disinfected, by treating your cat for both worm and fleas (which can carry tapeworm eggs) regularly and/or promptly, and also washing your hands thoroughly before you eat anything..
A vast amount of this information comes from an article by the RSPCA called Get Worm Wise. Thank you RSPCA.