A winter tyre is a tyre that has been designed with winter in mind. It has been optimized to work at the temperatures that are prevalent during the winter season and for snowy, slushy and icy conditions.
When it has been designed they use a rubber compound that will remain soft and flexible at very low temperatures as well as have the tread design that will have good grip on slippery surfaces.
Winter tyres comprises both studded tyres, that are only to be used during the winter season and then non-studded tyres. Most non studded tyres should only be used during the winter season, but you do have some all-weather tyres that are approved for winter use, but can also be used in all other seasons too.
Tyres that have been approved for winter driving have a symbol on the sidewall, depicting a snowflake inside a mountaintop with 3 peaks. It is not enough to have the M+S symbol on the sidewall, as not all M+S symbol tyres are approved for winter driving. So if you want to drive in winter conditions, make sure that it has the winter-approved symbol.