Well, offset is a number, that influences the song depending on the number you set it on. Fe. if you have set your offset to + 50, the beat on the certain object will appear after you've clicked the object. That means you will click on the object, and after that you'll hear the beat, which was supposed to be on that object. If the offset is -50, the beat will appear before the time you should press the object. So you will first hear the beat a little bit sooner, than you normally would without the offset.
Offset can sometimes help you, though it differs from person to person. Someone uses it, someone doesn't. It depends on your personal preference.
You can change your offset in options (that change will apply on all maps you're going to play until you change it again) or you can change it in-game by pressing the keys you've set your decrease local song offset and increase local song offset on (this method will only apply for that one specific map)