In general, rounding has the task to map a given number which cannot be exactly represented to the closest representable number. In that sense, rounding is uniquely defined this way, except for the nasty case where a given number x lies exactly between two representable numbers x0 and x1. For instance, if we would have no digits after the decimal point, the number 3.5 would have to be rounded to either 3.0 or 4.0.

Only in that case, the different rounding modes make a difference. We may now decide to always round to +oo, to -oo, or whatever the rounding modes determine as one of the two numbers x0 and x1. Round to nearest even will pick the one of x0 or x1 that has an even mantissa. In the above case, it would be 4.0 which is the even number of the two (note that one is always even and the other one is odd).