Standard deviation from Wikipedia :
In statistics and probability theory, the standard deviation
(represented by the Greek letter sigma, σ) shows how much variation or
dispersion from the average exists.1 A low standard deviation
indicates that the data points tend to be very close to the mean (also
called expected value); a high standard deviation indicates that the
data points are spread out over a large range of values.
In the case of stock returns, a lower value would indicate less volatility while a higher value would mean more volatility, which could be interpreted as high much change does the stock's price go through over time.
Mean would be interpreted as if all the figures had to be the same, what would they be? So if a stock returns 10% each year for 3 years in a row, then 10% would be the mean or average return. Now, it is worth noting that there are more than a few calculations that may be done to derive a mean. First, there is the straight forward sum and division by the number of elements idea. For example, if the returns by year were 0%, 10%, and 20% then one may take the sum of 30% and divide by 3 to get a simple mean of 10%. However, some people would rather look at a Compound Annual Growth Rate which in this case would mean multiplying the returns together so 1*(1+.1)*(1+.2)=1.1*1.2=1.32 or 32% since there is some compounding here. Now, instead of dividing a cubic root is taken to get approximately 9.7% average annual return that is a bit lower yet if you compound it over 3 years it will get up to 32% as 10% compounded over 3 years would be 33.1% as (1.1)^3=1.331.
Sharpe Ratio from Investopedia:
A ratio developed by Nobel laureate William F. Sharpe to measure
risk-adjusted performance. The Sharpe ratio is calculated by
subtracting the risk-free rate - such as that of the 10-year U.S.
Treasury bond - from the rate of return for a portfolio and dividing
the result by the standard deviation of the portfolio returns.
Thus, this is a way to think about given the volatility how much better did the portfolio do than the 10 year bond.
R-squared, Alpha and Beta:
These are all around the idea of "linear regression" modelling. The idea is to take some standard like say the "S & P 500" in the case of US stocks and see how well does the portfolio follow this and what if one were to use a linear model are the multipliers and addition components to it.
R-squared can be thought of it as a measure as to how good is the fit on a scale of 0 to 1. An S & P 500 index fund may well have an R-squared of 1.00 or 0.99 to the index as it will track it extremely closely while other investments may not follow that well at all. Part of modern portfolio theory would be to have asset classes that move independently of each other and thus would have a lower R-squared so that the movement of the index doesn't indicate how an investment will do.
Now, as for alpha and beta, do you remember the formula for a line in slope-intercept form, where y is the portfolio's return and x is the index's return:
In this situation m is beta which is the multiple of the return, and b is the alpha or how much additional return one gets without the multiple.
Going back to an index fund example, m will be near 1 and b will be near 0 and there isn't anything being done and so the portfolio's return computed based on the index's return is simply y=x. Other mutual funds may try to have a high alpha as this is seen as the risk-free return as there isn't the ups and downs of the market here. Other mutual funds may go for a high beta so that there is volatility for investors to handle.