The key feature for me is that you can access messages through a web app, and through native desktop apps on Mac and Windows. This means that I can really use it with people who aren't on Macs/iOS all day for iMessage, which is most of the world outside of tech unfortunately.
The open protocol means that anyone can write their own client and pull out message transcripts.
The business model is a little sketchy (donated Russian social network money I think) but at some level who cares: if it disappears I can just switch to something else (that probably won't be as good unfortunately).
I know there has been some controversy about their encryption, but I would not trust any IM platform with perfect security. I care much more about reliability and availability on multiple platforms, which is where Telegram wins hands down.