What you need to bring to Svalbard depends on the season and what activities you want to do. You can read more about the temperatures and how the weather changes from month to month here. During summer it is usually between 3 - 7 degrees. There may be snow in the mountains, so if you're going hiking, bring sturdy, waterproof hiking boots. During winter the temperature is between -10 and -30 degrees. The windchill adds to the freezing temperatures, so dress very warmly!
Remember that a passport or a Norwegian national ID card is required to travel to Svalbard.