Doubles can only store a certain amount of digits. If you have a decimal with an unlimited amount of digits(eg. 1/3 or sqrt 2), then the computer can't possibly store all the digits. So you can get a lot of rounding errors with doubles. If you use == for comparing doubles, like so...

double d1 = blahblahblah;
double d2 = asdfjkl;
if(d1==d2){
   ...
}

Then you can run into a lot of issues, even when d1 and d2 should be equal. The safer way is to create a tolerance value epsilon. You can imagine it like an error margin: for 2 doubles to be equal, they must have an error margin of epsilon or less:

double EPS = 1e-9; //I usually use 1e-9, just to be safe on rounding errors
double d1 = blahblahblah;
double d2 = asdfjkl;
if( abs(d1-d2)<EPS){
   ...
}

This type of comparison will save you on a lot of problems.