To disrupt is to interrupt or throw something into disorder. If you don't turn your phone off before a play, it might ring and disrupt the actors and the audience.
Disrupt goes back to the Latin root disrumpere, "to break apart." When you disrupt, you break someone's concentration, break up a routine, or break apart a system or order, as when bad weather disrupts the travel plans of people in airports. Even if your headphones keep the music in your ears only, singing out loud can disrupt those around you. A larger interruption would be if a war were to erupt. That would disrupt the peace of an entire region and its people.