How would "Turnover rate" effect my investment?

I notice there are many funds has some number call "Turnover rate" how would that effect my investment?
And also, what is Beta, R-squared and standard Deviation mean to me?
Are they important?

beta
Definition

A quantitative measure of the volatility of a given stock, mutual fund, or portfolio, relative to the overall market, usually the S&P 500. Specifically, the performance the stock, fund or portfolio has experienced in the last 5 years as the S&P moved 1% up or down. A beta above 1 is more volatile than the overall market, while a beta below 1 is less volatile.

r-squared
Definition

A measurement of how closely a portfolio's performance correlates with the performance of a benchmark index, such as the S&P 500, and thus a measurement of what portion of its performance can be explained by the performance of the overall market or index. Values for r-squared range from 0 to 1, where 0 indicates no correlation and 1 indicates perfect correlation

The web site below is a good source for definitions of financial terms.

Turnover - is a measure of how frequently the portfolio manager buys and sells the securities in a mutual fund .This causes two problems:

1. The fund can generate a lot of short term gains. These are taxed at a higher rate than long term capital gains. This is only a problem in a taxable account not an IRA
2. The bigger problem with high turnover is that it drives up the commission costs that the fund must pay. These costs can be a real drag on the fund's performance and are not included in the expense ratio's publised. So when an actively managed mutual fund quotes it's expense ratio as 1% it may also include another 1% for commsiions. That cuts your return by 2%. With an index fund there is very little turnover so their expense ratio is pretty close to the actual expenses.

If an financal advisor buys and sells stocks in a customer account too frequently that is usually referred to as churning

Turnover rate means someone else is doing your trading or managing a mutual fund ,
( I avoid that like the plague ) .
But the more turnover they have , the more the trader can make in commissions , leaving less $$$ in the fund .
In individual cases , some brokers have nearly drained a client's account just from excessive trading to get the fees / commissions .

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I think kate has mixed up stock "Churning" with mutual fund turnover rate. All mutual funds have a turnover rate.
Effects your investment in two bad ways.
1) Higher turnover rate means the fund buys and sells more stocks quicker and therefore pays out higher brokerage fees. Those fees come out of YOUR total return (at the end of the year the price you could sell the fund for {net asset value} therefor the value of the fund will be less.
2) A high turnover rate fund may have more total capital gains and more short term (taxed at a higher rate than long term capital gains) capital gains to distribute to you so you pay more taxes now.
And one good way (if the manager is any good). A low turnover fund may invest in slow growing blue chip stocks with a (after all fees are paid) 8% total return. A high turnover fund, may just be investing in the hot high growth tech/alternate enegy/biotech/nanotech type stocks. If the manager is very good, he will buy low and sell high and give you a total (after fee) return of 15% or more. Even with the higher taxes you pay now, you may still have more money in your pocket at the end of the year.