1. it is an open standard based on free software
2. it is based on history synchronization between servers instead of message transmission between clients, so you can send messages seamlessly from any device and have access to your conversation history (think git vs sms)
3. you can use your own server to host your conversations (the conversation history is replicated on the server of each participant)
4. it has end-to-end encryption
5. there is only one type of conversation, so the are no differences between a one-to-one chat and group chat: a one-to-one chat is simply a group chat with only two participants
i have my own personal server (old laptop at home), and the rest of my family uses another dedicated server (other old laptop at my cousin’s home). friends and coworkers use the matrix.org homeserver. the matrix.org homeserver can be slow sometimes (because it hosts many rooms and has many connected users), but messaging between our own servers is instant.
sure, it’s not (yet) as polished as mainstream apps. for example, currently, with end-to-end encryption, one need to verify each device of each other person on each of their own devices, which is not very user friendly (but this is being worked on, so only one verification per person will be needed in the future).
this said, it has nevertheless the most needed features. it has even some features that mainstream apps lack. for example, if you’re a little technical you can start using bridges. this allows to receive and send messages from/to other messaging systems (irc, xmpp, slack, telegram, discord, sms,…) all from within your matrix client.