Repurposing your content means quite simply to change the content so that it can be used for a different purpose.  To break this concept down here are a few examples.
Let’s say you do a online presentation. While you’re giving the presentation, you could be recording your screen as you give your presentation. You can take that recording, separate the audio portion and make it into a podcast. You can take the visual portion or just the slides and put that up on SlideShare. You can take the complete audio/video recording and post it to YouTube, Vimeo and other video hubs. Lastly you can add the recording as a digital product or online course.
So,with just one little thing such as a presentation can be repurposed and put into other media.
Additional repurposing examples using that same presentation. You take the audio format, transcribe that into text using company like SpeakerText and now you have a transcript of your audio. So, now with the written word you could create an eBook or multiple blog posts. Another option is creating infographics.
Now, the simple reason to repurpose your content is to reach a wider audience. Not everyone is going to be on SlideShare, or YouTube, etc. With a wider audience, you have more opportunity get your message or your brand across to various potential customers and clients.  You can reach your audience on their medium of choice.