First lets understand what convexity means:
convexity refers to non-linearities in a financial model. In other
words, if the price of an underlying variable changes, the price of an
output does not change linearly, but depends on the second derivative
(or, loosely speaking, higher-order terms) of the modeling function.
Geometrically, the model is no longer flat but curved, and the degree
of curvature is called the convexity.
Okay so for us idiots this means: if the price of ABC (we will call P) is determined by X and Y. Then if X decreases by 5 then the value of P might not necessarily decrease by 5 but instead is also dependent on Y (wtf$%#! is Y?, who cares, its not important for us to know, we can understand what convexity is without knowing the math behind it). So if we chart this the line would look like a curve.
(clearly this is an over simplification of the math involved but it gives us an idea)
So now in terms of options, convexity is also known as gamma, it will probably be easier to talk about gamma instead of using a confusing word like convexity(gamma is the convexity of options).
So lets define Gamma:
Gamma - The rate of change for delta with respect to the underlying asset's price.
So the gamma of an option indicates how the delta of an option will change relative to a 1 point move in the underlying asset. In other words, the Gamma shows the option delta's sensitivity to market price changes.
Gamma shows how volatile an option is relative to movements in the underlying asset.
So the answer is:
If we are long gamma (convexity of an option) it simply means we are betting on higher volatility in the underlying asset(in your case the VIX).
Really that simple? Well kinda, to fully understand how this works you really need to understand the math behind it. But yes being long gamma means being long volatility.
An example of being "long gamma" is a "long straddle"
I personally do trade the VIX and it can be very volatile, you can make or lose lots of money very quickly trading VIX options.
What does it mean to be "long gamma" in options trading?
Long Gamma – How to Make a Long Gamma Position Work for You
Delta - Investopedia
Straddles & Strangles - further reading if your interested.
Carry(investment) - even more reading.