Smearing in everyday language means to "coat or mark (something) messily or carelessly with a greasy or sticky substance". For example draw a line with paint, and then with your finger "smear" it to make it mathematically less defined.
In physics the use means to impose an envelope, so that the clean mathematical definition of a trajectory, for example, is extended to probable points due to some physical function guessed at or derived. so instead of getting a trajectory $f(x,y,z){}$ you get a smeared trajectory, with an uncertainty around each $x,y,z$, due to the uncertainties in the measurements or original assumptions. It is a way of introducing errors in measurements.
Gaussians are used because it is a shape describing random states. If though a detector has a particular bias so that the errors introduced are not random, a different function will be used for the smearing.
The process is necessary because we cannot have perfect measurements, and to compare with theory we have to introduce the errors. In monte carlo this is done with smearing the ideal event values by the detector uncertainties.
