In very simple terms, these are all leveraged exchange traded funds. This means that each of these instruments, which trade like stocks, will move more than the indexes on which they are based.
For example, TVIX is derivative of the VIX, which generally measures the overall volatility of the market. When the market goes up, the VIX tends to move down. When the market goes down, the VIX tends to move up. But TVIX, because it is 2-times the leverage, will move twice the level of the VIX. Trading leveraged funds based on the VIX (there are many of them) has become very popular, because of the intraday volatility provided by the instruments. (Pull up a chart of the VIX (which is a measure, not a stock), and a chart of the S&P 500, and put them side by side. You will see how how they generally move inverse to each other.)
DGAZ and UGAZ are leveraged to natural gas prices. They are 3-times leveraged, which means they move with great volatility. They are related to weather only in that some traders assume the price of natural gas may rise or fall depending on weather forecasts. But playing these instruments in regard to the weather is a game for serious pros who are plugged into historical models.
I would caution you VERY STRONGLY against getting heavily involved in any of these instruments until you are well-versed in what they are, and how they trade. And even at an expert level, you don't want to hold any of these overnight or over weekends unless you have a well researched plan in place and fully understand your risks.
Don't even get me started on the 'Contango' effect.
Good Luck.
News 
Market Data 
Discover 
