In the broadest terms, you can say that investment is the giving up of some resource in order to gain some resource in the future. In our society, we usually think of investment in terms of spending money in hopes of getting a larger amount of money later.
But are investments by individuals also investments by society as a whole? Are resources a zero-sum game, or can the size of the whole pie increase? I would propose that we should make a distinction between investments that just move resources around without changing the total amount of resources, and investments that increase the total amount of resources.
When you buy stock in a publicly held company, are you investing in increasing resources? Usually, the answer is no. The money you use to buy the stock usually does not go to the company, but to the previous owner. If you are buying an initial stock offering, or a sale of new stock, the company might use that money to fund expansion. The main useful function of the public stock market is to provide liquidity for the initial investors, so that they can cash in on the initial investment. If you invested in Apple in the early 1980s, you were helping build the company. If you invest in Apple now, you are just moving money around. Apple has huge cash reserves, they can fund any R&D or expansion they want without having to raise any more money from the financial markets.
But many activities of the financial market don't help liquidity much, they just move money around. Short selling is a zero sum game, any gain from a short seller comes from a loss from someone else. The new very high frequency trading computer systems just skim a bit off of a huge number of transactions. I cannot think of any way in which these high frequency trading systems can help increase the overall wealth of society.
The infamous credit default swaps are another example of such zero-sum investments. Not only do these things not increase resources, but we have seen how they can actually sabotage resource production.
But to me, the ultimate example of non-productive investment is gold. Gold would be a useful metal if no one thought it was money. Gold is perfect for electronics, if it was common enough, we would be using it to solder circuit boards instead of lead. If you buy gold as a precious metal, it is a zero sum game that cannot increase the wealth of society. Because a lot of people think that gold is money, they want to invest in gold. But money is whatever people agree is money. Money is just a tool to allow resources to be exchanged that is necessary in any economy large enough that barter would not work. When money becomes an end in itself, with a financialized economy where manipulating money is more important than actual goods and services, then the economy is in trouble, as recent history shows.
There is so much useful investment that needs to be made now. Imagine if entities both public and private spent a lot of money, even if much of it is borrowed, on schools, teachers, roads, railroads, wind turbines, smart electric grids, scientific research of all types, and many other useful things. Now imagine if the same entities, with the same amount of money and borrowing, used the money to buy gold. In which scenario would society be better off?