Adjusted Closing Price
  
On any day, you can look up a stock’s closing price and get one number. Clear as clear can be, right?
Not so fast. Closing price can be one number, but it can be affected behind the scenes by corporate stuff like rights offerings, dividends, stock splits, and other corporate actions. The closing price, if it's affected by this stuff, gets adjusted to reflect said actions.
A famous example is the one-time enormous dividend made by MSFT (Microsoft) when Bill Gates retired from the CEO role. That little action required some adjusting. Without it, the closing price of MSFT would have looked less spectacular than it really was.
BTW, adjusted closing price is important when looking at historic closing prices or when doing analysis on historic returns. If you're just an average investor, though, you probably won't even run into it.