Soft mod is the process in which you trick a console into allowing you to run homebrew applications. For example there are a few ways to Soft mod the Xbox that allow you to run EvolutionX (a.k.a. EvoX). From there tons of other applications that can run on a PC will run from the Xbox.
Soft modding does not require you to open up the case of the console. It may be required that you have to buy additional peripherals like Action Replay and a particular game to allow the programs their "in".