Why would you want to exercise an in-the-money option?
Although we know (perhaps better than most) that there are many uses of stock options, we tend to focus quite a bit on using options to speculate -- in which case traders are typically buying and selling the options contracts themselves, without ever touching the underlying shares. However, option buyers do have the right to use their call and put options as a means of buying and selling shares, through a mechanism known as "options exercise."
Specifically, when a call or put option is in the money at or before its expiration date, the holder of that option can exercise their right to buy (in the case of a call) or sell (in the case of a put) 100 shares per contract of the underlying stock at the strike price of the option. As such, exercising an in-the-money call option would allow the trader to buy shares at a discount to the current market price, while exercising an in-the-money put would mean selling the shares at a higher price than what they're currently commanding on Wall Street.
As noted above, many of the options traded are never exercised, as traders instead seek to profit from changes in the value of the option itself -- known as "trading premium." However, traders should be aware that options that are in the money are subject to automatic exercise if they're not closed out prior to expiration. (Option contracts that are at-the-money or out-of-the-money at expiration will expire worthless, with no further action required to exit the trade.)
Let's look at an example of trading premium vs. exercising an option. Stock XYZ was trading at $50, and an investor bought to open an April 50 call for $3. The stock gets upgraded by analysts and rallies to $60 before the April expiration date. What should the giddy trader do? They could sell to close the call, netting a profit of $725 ($10 in intrinsic value + $0.25 in time value - $3 premium paid = $7.25 * 100 shares per contract).
Or, they could exercise the call and buy 100 shares of XYZ for $50 apiece, or $5,000. The trader could then either hold onto the shares of XYZ as part of a longer-term bullish forecast, or turn right around to sell them at the market value of $60 apiece, or $6,000. After subtracting the initial $300 cost of the call, the profit on the latter scenario would be $700 (or $6,000 - $5,000 - $300). That's $25 less than the premium-trading scenario, since the remaining time value is essentially forfeited -- and that's prior to considering the additional brokerage fees involved.
However, if over the course of the options trade your forecast on the underlying has shifted from "betting on a short-term bounce" to "convinced of the long-term prospects," exercising an in-the-money call provides a valuable opportunity to buy the shares at a discount -- which then allows you to participate in any corresponding shareholder benefits, such as dividends and voting rights, that are not available to options holders.
Another reason to exercise would be in the case of a put hedge on a long stock position. If one of these "married puts" is in the money, it's likely because the shares have breached a technical threshold below which the investor would rather not own the stock -- and so the ability to sell the shares at the option's strike price via exercise effectively serves as an exit strategy for the stock investment.