Cont. is a short written form of continued. You meet it at the foot of a page, under a heading, or on a form, pointing you to the rest of the text: 'cont. on p. 8.' People who make newspapers, school worksheets, and meeting notes use it to save space. You do not say 'cont.' as its own word; if you are reading the page aloud, you say 'continued.' Though actually, English cannot even agree how to cut it. Some pages write cont., some write contd., some write cont'd with a little mark, and some just write continued. They all mean 'this goes on.' It belongs to paper and PDFs, not to chat and not to speech. A show that says 'to be continued' is promising a later part; cont. is the cramped cousin on the page you are already holding.