What's the difference betweeng "matching" the market and "beating" the market?
If your returns match the market, that means their rate of return is the same as the market in question. If your returns beat the market, that means their rate of return is higher.
There's no one 'market', mind you. I invest in mutual funds that track the S&P500 (which is, very roughly, the U.S. stock market), that track the Canadian stock market, that track the international stock market, and which track the Canadian bond market.
In general, you should be deeply dubious of any advertised investment option that promises to beat the market. It's certainly possible to do so. If you buy a single stock, for example, that stock may go up by 40% over the course of a year while the market may go up by 5%. However, you are likely taking on substantially more risk. So there's a very good chance (likely, a greater chance) that the investment would go down, losing you money.
"Beating the market" is a difficult phrase to analyze. It can be used to refer to two different situations:
1) An investor, portfolio manager, fund or other investment specialist produces a better return than the market average. The market average can be calculated in many ways, but usually a benchmark - such as the S&P 500 or the Dow Jones Industrial Average index - is a good representation of the market average. If your returns exceed the percentage return of the chosen benchmark, you have beaten the market - congrats! (To learn more, read Benchmark Your Returns With Indexes.)
2) A company's earnings, sales or some other valuation metric is superior to that of other companies in its industry.
Matching the market, I would presume will be generating returns equivalent to the index you are comparing your portfolio with. If for a sector/industry then it would be the returns generated by the sector/industry. As an index is more or less a juxtaposition of the market as a whole, people tend to use an index.
There was a time when everyone felt their goal was to beat the respective index they followed. But of course, in aggregate, that's a mathematical impossibility. The result was that the average say large cap fund, whose benchmark index would be the S&P, would lag on average by 1-2%.
A trend toward ETFs that would match the market had begun, and the current ETFs that follow the S&P are sub .1% expense.
For the fact that studies (Google "Dalbar" for examples) show the typical investor lags not by 1% or 2%, but by far more for reasons of bad timing, my own statement that "I've gotten a return these past years of .06% less than the S&P" would have been seen many years ago as failure, now it's bragging. It handily beats the typical investor and yet, can be had by anyone wishing to stay the course, keep the ETF very long term.