In simple finance, being long an asset, say a stock, means buying it. However, if we look a bit deeper into matters, the term long has a more general meaning:

A long exposure to an underlying means that you make money when the underlying rises in value, and lose money when it falls in value.

The term "underlying" here is a bit of an umbrella term that can mean things like stocks, bonds, commodities, or other assets. The most obvious way to be long is, indeed, by just buying the underlying. If I, for instance, buy 400 shares of Exxon, I am long 400 shares of Exxon. If the price of a share of Exxon rises by a dollar, I've made 400 x $ 1 = $ 400.

However, the definition is a bit more generic than that. Derivatives allow me to generate a long exposure without actually owning the asset. For instance, imagine I buy a call option on Exxon, allowing me to buy the share at a certain price, say $ 75 (The price of an Exxon share at the moment of making this WU is $ 76.11). Now, if the price of Exxon rises, buying a share at $75 becomes more attractive. If it rises to $ 80, I would make 5 dollars when I exercise the option. The precise relation between the price of an option and the price of the underlying is very complex, but we can state that a rising share price increases the value of the call, as seen above. When the Exxon share price drops, it will be less likely I can buy Exxon at a price below the current market price and make money. Hence, when the price of Exxon drops, my call will be worth less and I will lose money. Because I make money when Exxon rises and lose money when it falls, being long a call means I'm long Exxon.

A second example would be selling a put option. Imagine I sell the 75 put in Exxon. This means that I am obliged to buy Exxon at 75 if the person to whom I sold the put wants this. Now, as long as Exxon is above 75, I'm pretty much safe, and the more the price of Exxon rises, the less likely I am to have to buy the shares at 75 with a potential loss. Hence, if Exxon rises, I make money because the value of the option I am short diminishes: I am less likely to suffer a loss. By a similar argument, I am more likely to buy the Exxon shares at a loss if the shares fall; hence, when the price of Exxon drops, I lose money. Hence, I am long. Apart from these two examples, there are many, many more ways of generating a long exposure to an underlying using derivatives; you can make it as complex as you want.

Having established what a long position is and how to get one, the next step would be to identify why we want one. Essentially, one would want a long position if one would think that the price of an asset will go up. A very common position is being long shares, because for the last century or so, the long-term trend of shares is up. For a true investor, the long position is the natural position to be in. Another advantage of a (unleveraged long position is that your maximum loss is limited to the money you spent on the position.

Summarizing, being long an asset means that if the asset rises, you make money. This can be achieved by just buying the asset, but it can also be done with derivatives. In the latter case, it's not always easy to know exactly how much you are long. A long position is very common in investing, as many assets have a tendency to rise in price over time. The long position profits from this.