Volatility is your first measure of risk.
It is an indication as to how far a company or instrument might move up or down versus its mean or its average.
Very simply put, the higher a stock or instrument's volatility, the riskier it may be, or the more chance it might fall from its average price.
A large-cap or mega-cap stock would, typically, have a lower volatility than a small-cap or less well-traded stock, therefore, giving you an indication of the amount of risk that you might be incurring in buying a small company that might move up or down more dramatically during a given day than a large-cap stock which might move up or down less during a course of any given day.
When thinking about portfolio construction, you've got to add together the volatilities of the underlying companies in your portfolio, which is why we talk about diversification and the reduction of volatility through the addition of names, or diversification.
Volatility is important, you need to think about it before starting to invest because it gives you an indication of the amount of money that you might lose on average. We talk about volatility in terms of confidence intervals.
For example, a 95% confidence interval would tell you that something might happen within that range 95% of the time. But remember the 5%! The 5% is where you might expect it to do something very different.
So when thinking about investing, think about the volatility of both the stock that you're investing in, the portfolio in which it sits, and the aggregate volatility of your overall portfolio, because it will give you a sense as to the amount both you might make but also that you might lose.
To learn more about risk, visit this page.