Vanguard was founded by a famous American investment guru called John C. Bogle. During some undergrad research he discovered that various investment funds had not done any better than the general Indexes. An Index is a list of companies in a certain category as a way of following general price trends in that category. So for example the S & P 500 index follows the fate of 500 of the largest American companies. It's a way of following the general trend of the overall stock market in a certain category. A well known Index in the UK is the FTSE 100 which you will often see in the news footer trailing financial news. It's a measurement that gives you a good general idea of the price and health of the UK stock market at a given moment. Indexes don't contain EVERY stock in a given stock market, but they usually list the big players in that particular category, whatever it is you are measuring. They are often used as a benchmark for the general health of the stock market and economy and which as an investor you can compare your own investments against.
Investment vehicles such as a Mutual Fund where many small investors (such as you and I) pool all our money are usually managed by investment fund managers who pick a range of stocks they hope will perform well in the long term.
Bogle discovered that rather than worry about picking the right stocks and paying fees to a third party to manage your stock for you, investors could be just as successful by investing in all the companies in an index and just letting the stock follow the index up and down. This is called an Index Fund. Due to its simplicity there is no need for expensive management and it is a simple investment that everyone can understand. It's also easy to know how well your fund is doing. There are some fees and costs involved with Index Funds but they are generally much cheaper than other similar investments. So Bogle was on the side of the investor, keeping as much of your money in the investment and less on fees.
So by investing in a general Index you are investing in the general health of the economy and in the prominent companies in the economy. If you think that over time (decades) the economy will get stronger and these companies will continue to be big players, your investment is following a much broader, overall bet that overtime the economy will be worth more than it is today. Up until our current world crisis, as the world economy grew and inflation cheapened money over time, long term, the stock market went up.
However, I do think the world economy will change now in ways we can't imagine. Some very big companies are now in very serious trouble and others are doing spectacularly well. So by nature the stock market is volatile and this is probably going to be the most volatile time we have ever seen in the next couple of years. This would not be the time to put lots of money in that you want you take out in the next 5 or even 10 years. But 15+ years for building wealth over the long term is more the horizon you need to be thinking for most stock market investing, for retirement or other large financial goals.