BitInstant was a service started in 2011 by Gareth Nelson and Charlie Shrem aiming to help make faster fiat deposits into a few Bitcoin exchanges, such as MtGox, BitStamp or VirVox. At some point you could also convert the deposits directly into BTC. BitInstant would handle cash deposits from places like Walmart and credit you appropriately.
Overall, it seemed like an approachable way to get some bitcoins back in the day when a lot of the Bitcoin exchanges were struggling with accepting funds in the US.
It seems there was a lot of demand for this service in 2013, but unfortunately the site was shut down after its CEO got arrested in early 2014.
Now, what I just described doesn't sound all that interesting in 2018 - we currently have a lot more payment options available now that fewer banks are afraid of Bitcoin. However, BitInstant had one more underappreciated feature I wanted to talk about...
BitInstant not only did normal cash deposits, but it also allowed you to redeem coupons from MtGox, VouchX or BTC-e and use those as a deposit methods into the above mentioned exchanges. In other words, you could use it to transfer money from BTC-e into BitStamp, or from MtGox into VirVox. This would allow you to handle arbitrage between the exchanges much more easily.
It seems these days there aren't as many options for that. Last time I checked I could find about three exchanges that would take BTC-e coupons as a deposit method and you can use Tether across a number of exchanges as a substitute for USD, but there isn't a neat way of transferring fiat between exchanges in a really fast manner.
I suppose you soon won't need a service for transferring bitcoins between exchanges if the Lightning Network can deliver its instant transfers on mainnet. Some other alts might benefit from something like voting pools though.
A service that would allow you to transfer fiat between any exchanges might make for a more efficient market - imagine being able to take advantage of some of the more recent arbitrate opportunities. The prices would be more uniform around the world and everyone would be getting a more fair deal.
The solution wouldn't even be that hard to implement - the major complexity would come from having to handle the large, international capital transfers to balance the books every now and then. So once again, it comes down to the inefficiencies of the traditional banking system...
BitInstant was an interesting "old" service in the Bitcoin space that helped people deposit their money onto a few crypto exchanges. It also provided a way to move funds between crypto exchanges, providing some way of cashing in on some arbitrage opportunities. Unfortunately, there aren't that many ways of transferring fiat efficiently between the major exchanges these days.