Lets look at two sets of numbers. The big difference between these sets of numbers is their standard deviation. That just tells us that the second set is much more variable than the first. If you had a bit of risk capital to toss away and you wanted the opportunity to make some real money you might try set no. 2. But if you had any interest at all in capital preservation you would opt for set no. 1.
Standard deviation does make some intuitive sense as a measure of risk.
Standard Deviation allows us, with a few assumptions, to make a guess. The biggest assumption is that these numbers are normally distributed about the mean. That says that the numbers cluster around the mean and thin out as you get further away from the mean. The standard deviation could be thought of as how quickly these numbers thin out. The other big assumption is that we have enough numbers in our sample to make the guess reasonable.