@daredevil_kohai has already mentioned several. What I most like about Telegram, though it does require a phone number to get started, is that it allows messaging anyone else without revealing one's phone number with the use of usernames. For me my phone number is a precious piece of information that I guard (despite the fact that I still get spam SMS and such) because it's increasingly used in many contexts as a unique person identifier for behavior profiling and surveillance (which I'm against). With Telegram, I do have to trust the platform on not leaking my number, but that's the extent of my worry.
Wire went two steps further and allows a) signing up with email addresses (without revealing phone number to Wire) and more recently b) multiple accounts for a person. Telegram has just started catching up on multiple accounts, but is still tied to a phone number.
A minor feature in Telegram that I use a lot is to edit my messages after sending them. No more re-typing messages with corrected typos prefixed with an asterisk. This either doesn't exist or came much later in other platforms I've listed in my comment (including WhatsApp).
This is anecdotal, sharing photos in Telegram means it gets through with the same resolution instead of being re-compressed and losing detail. I've heard from some others that re-compression happens on other platforms, but I don't recall on which ones right now.
Speed of message delivery, which is the most basic thing for any messaging platform. While Telegram has slowed down over time (it used to be almost instantaneous a few years ago), it still seems faster than the other platforms. This may just be my experience, since there are multiple factors that affect this.
Multi-platform and multi-device support with synced conversations across all of them. Telegram did it this way from the beginning. Wire is also similar, and better, since it has end-to-end encryption as well (but it doesn't store all conversations forever, and so newer devices will start with the most recent messages). Signal is way too behind in this department, and doesn't even allow carrying over received messages from one phone to a newer phone (this is true in iOS, and on Android it involves some work by the user). Signal actively prevents data from being backed up from the device!
Telegram's search, both within conversations and across conversations, is very fast and reliable.
Telegram allows chatting with oneself, which was renamed to Saved Messages a little while ago. I use it as a bookmarking feature to store interesting information. Combined with great search, it becomes a reference repository.
I'm sure I'm forgetting some other stuff, but the overall user experience is much better, right from application startup.