Cover in the context of finance is used to refer to any number of actions that reduce an investor’s exposure. The term cover is distinct from coverage, which, in the world of finance, refers to insurance coverage in addition to referring to the financial ratios that measure a company's margin of safety in servicing its debt and making dividend payments. Cover can also be used without context to simply mean the act of protecting overall portfolio value, as in providing cover against market volatility.
Cover basically means taking action to decrease a particular liability or obligation. In many cases, this means completing an offsetting transaction. For example, if an investor is shorting a stock and wants to eliminate the risk of a short squeeze, then she will buy to cover. This means she will purchase an equal number of shares to cover the shares she has shorted without owning.
Closing out a position and covering a position can be the exact same thing in finance, but the two phrases have different connotations. In the buy to cover example above, the investor could choose to close the position by delivering the shares or she could let it run knowing that she now holds the shares to cover it. The act of covering does not necessarily mean closing the position. To cover is to take a defensive action to lower the risk exposure of a position, investment or portfolio of investments. Close or closing, by contrast, suggests that the risk is being fully eliminated by exiting the position creating exposure.
Cover has a few well defined uses in finance, and there are a wealth of less well defined uses also. In futures trading, cover can be used to describe buying back a contract sold earlier to eliminate the obligation. This is done when the market conditions that the contract seller was expecting clearly aren't coming.
In addition to the previously discussed buy to cover, there is also sell to cover. Sell to cover refers to employees with stock options that are in the money cashing them in and then immediately selling a portion of the stock to cover the cost of buying them. For example, imagine an employee has a stock option for 200 shares at $25 per share, and the stock currently trades for $50 a share. The employee will exercise the option, paying $5,000 for 200 shares ($25 x 200) and then sell 100 shares at the market price of $50 to cover the cost of the purchase. This scenario ends with the employee owning 100 shares that were essentially free.