There are three key variables to consider when choosing violin strings; core type, gauge and tension.
For centuries, strings could only be made with gut core, from sheep intestine. Gut core violin strings have the warmest sound, complex and rich with overtones and are used primarily by professional classical musicians. These strings can be difficult in terms of over-sensitivity to temperature and time needed to settle in and maintain pitch. With developments in technology in the last 50 years, synthetic core strings are now available, which, as closely as possible, replicate the tone and feel of the gut core string, while avoiding some of its disadvantages. The other option is a a steel core string, which, like a guitar string, is comprised of a straight or twisted wire, wound with metal. These are the most stable and durable and offer stable pitch, high volume, but less overtones. These are favoured by fiddlers and contemporary players.
The most commonly made violin string gauges are light, medium and heavy, but many string makers offer variations using gauge numbers. As a general rule, heavier strings produce more tone, but have a slower response, and thinner strings have a fast response but have a less full, lower volume sound.