1) Post quick hair, make-up tutorials, how-tos,
Sometimes it seems like such an investment to sit down and watch a full YouTube video, and it requires going to an external site. Blah. I'm lazy. If I'm already scrolling through your feed on Instagram when I'm bored, I'll probably watch your 15 second tutorial on victory rolls. PLUS, as a blogger, I'm more likely to post a quick 15 second video of how I do my hair rather than setting up the tripod and doing a full one. I've already noticed people using Instagram instead of DSLRs for their outfit posts - I suspect video tutorials will soon follow.
The best thing is if you use something like FollowGram.me, you can embed your video in your blog. See my poor example below.
2) Bye-bye long-winded descriptions, hello talkies
I'm sorry, but sometimes I don't want to read your 100-word description on Instagram on the story of how you bought your shoes or found the love of your life or your latest cooking concoction. Use your voice to tell the story instead, and use the description for #allthehashtags.
Show a video of taking that super-cute fabric and turning it into a circle skirt (Instagram allows you to upload videos you already took), or, more practically, a time-lapse of muffins from flour and batter to delicious crumbs.
You already use Instagram, so you'll probably use the video features. Chances are you're also more active on Facebook than on Twitter.
This is one way Instagram already has a leg up on Vine. Although Vine is made by the folks at Twitter, the apps are still separate. Instagram also has much better integration with Facebook (it embeds the video) than Vine does (you have to link to your tweet, and it opens up in a separate window).