The Real command puts the calculator in real number-only mode. This shouldn't be taken quite literally, as you can still type in i to get complex numbers, and do operations with them (they will be displayed as in A+bi mode, in that case). However, any operation done with real numbers that comes out to a complex result, such as taking the square root of a negative number, will throw a ERR:NONREAL ANS error.
There is no real advantage to using Real mode over a+bi mode -- it just adds another error condition that wouldn't be triggered otherwise. However, it is the default setting, and so there's a good chance that the calculator will be in Real mode when someone runs your program. Thus, when using complex numbers implicitly (such as in a quadratic equation solver) you should do something about this.
Rather than switch to a+bi mode, you might want to force the calculations to use complex numbers by making the original argument complex. The general way to do this is by adding +0i to the number. However, there may be an optimization in any particular case. See the Quadratic_Formula routine for a good example of this.
Real Done √(-1) (causes an error) √(-1+0i) i