It's been awhile since I used Briar, but unlike something like Signal, Briar is decentralized. So you can communicate with other Briar users in the absence of a central server. Briar at least used to be very strict about how you established contacts, so, for example, to add a contact you had to have them physically in your presence and exchange QR codes on your phone. You couldn't just add someone from your phone contacts, for example, or look up their phone number.
The downside to these things is that Briar tends to use up battery on mobile devices, because it's constantly running to handle the decentralized communications. Also, having to have someone physically in your presence makes it difficult to add someone casually like some other apps.
Some of these things might have changed, as they've been pretty consistent and active in developing the software, and it has evolved over time into offering more and more functionality. In general, Briar development tends to be very conservative about security, but also very encouraging of "robustness" development for lack of a better way of putting it (I think at one time they had an API so that it could be extended to general "off grid" communication protocols, or at least were discussing it).
I'm a little surprised it hasn't gotten more attention over the years, because I think it has been audited and seems very very secure. It also pops up on places like HN from time to time. On the other hand, that conservativism about security makes it sort of impractical for someone who, say, just wants to chat with friends and family.
I think the best comparison is probably with Matrix rather than Signal or Telegram, but Briar lacks the federated component at the moment.
This desktop release is interesting to me because in some ways it represents a major expansion of the software. As I said, they've tended to be very conservative and it's interesting to see it added. It also probably makes it more feasible to treat the desktop instance as a sort of "permanent on" server with access to a power supply instead of running off a battery (to be honest, starting with a desktop service kinda makes more sense to me given the power requirements).
Take this all with a grain of salt because, although I have it on my phone, I haven't actually used it in some time and haven't actively kept up with development in a couple of years.