VIX is the CBOE Volatility index, which attempts to track the volatility of the S&P 500, based on the implied volatility in the 30-day options of the S&P 500. Being an index, this is not a directly tradable instrument.
A quick word about implied volatility: an option’s theoretical price is determined by the underlying asset’s current price, the option strike price, the time until expiry, the risk-free interest rate, and the underlying asset’s volatility. For example, have a look at this Black-Scholes calculator. We can directly observe all of these input parameters, except for the volatility. By mathematically “reverse engineering” the volatility parameter from all of the other observed values, we obtain the implied volatility (i.e. what the market believes to be the volatility of the underlying asset).
If you're interested in the details of the VIX value calculation, you can have a look at the CBOE page that describes the steps of the calculation. It also explains the distinction, and relation, between the VIX volatility and the Black-Scholes implied volatility as discussed above.
In 2004, the VIX index became indirectly tradable through the introduction of Futures contracts. Since then, it is possible to speculate on the upcoming volatility for each month of the year (in fact, as of July 23rd 2015, there are also weekly contracts available). If you look at the CBOE VX Futures Daily Settlement Prices web page you can see the “current” prices for each of the upcoming futures contracts. For example:
This means that there is a VIX Futures contract set to expire at 01/17/2018 which is currently priced at 10.575 (and so forth). Notice that the prices, at the time of this writing, increase as we get farther and farther away from the expiry date. This is a consequence of investors' uncertainty about the future, and is called contango. It is conventional wisdom that we are in contango most of the time (in “normal” market periods). Once in a while, however, when investors start fearing near-immediate disaster, we can end up in what’s called backwardation: i.e. the futures set to expire soon are priced higher than the ones set to expire later.
A bit more terminology: the difference between the current price of a futures contract and the current spot price is called the basis. The spot price refers to the current price of the underlying asset (as opposed to the price of the futures contract on that asset). The VIX term structure refers to the shape made by the futures prices at different expiries (i.e. it is the term structure that can be in contango or backwardation).
Various exchange-traded funds and notes have since been created to replicate the VIX (or its inverse, with or without leverage):
If you're seeing this for the first time, you might be tempted to short and hold VXX. The fact is that most of the time you will be making quite a lot of money by doing that. However, it is an extremely risky strategy, as volatility spikes can be enormous, and can easily reach ~500%. Imagine the consequence of shorting VXX when volatility spikes by 500%... Update: if you held such a short position on VXX on February 6th, you'd be in trouble!
A trader might then wonder: do the VIX futures forecast the VIX spot price, or is it vice versa? Another way to put this is: does the futures basis have a predictive power on the spot price? Or, if the VIX futures tend to be mispriced and the spot price is a better predictor, does the basis have a (negative) predictive power on the upcoming changes in the price of the futures?
A study  was made to determine exactly that. Two distinct regression models were made:
(1) is a regression where we attempt to predict the upcoming change in the VIX spot price based on the current futures basis.
(2) is a regression where we attempt to predict the upcoming change in the VIX futures’ price based on the current futures basis.
The researchers' conclusion is that equation (2) is the statistically significant one, not (1). This suggests that VIX futures tend to be mispriced. It appears that there is a risk premium built into the price, possibly coming from the fact that these instruments are often used for hedging purposes. This also means that, from a trading perspective, when we are in contango, we should short the futures, because their price will decrease as we approach expiry. When we are in backwardation, we should buy the futures, because their price will increase as we approach expiry. Note that this strategy could theoretically be replicated by using one of the ETFs/ETNs, instead of the futures.
It should be noted, however, that this regression only explains about 10% of the variation in the futures’ price, which is why the researchers then goes on to isolate the risk premium by hedging against mini-S&P 500 futures. This should eliminate changes in portfolio value derived from overall volatility movements, since the S&P 500 is negatively correlated at about 80% with the VIX.
With a different methodology, another researcher  arrived at a similar conclusion: he rejected what he called the expectations hypothesis, i.e. the hypothesis that the VIX term structure reflects expected changes in the VIX.