Utreexo is a different way for nodes to keep track of which coins are spendable. Instead of generating a UTXO set from the history of all the blocks, utreexo introduces an accumulator that allow lightweight nodes to only keep track of small proofs for the coins they care about.
However, I think this also means that such light nodes could only interact with other nodes that speak utreexo, and wouldn't be able to have normal bitcoin nodes as peers (honestly, I'm not fully sure about this).
It seems to me that this creates a separate network -- in the same way that tor is a separate network from clearnet -- and I wonder what risks this might introduce into Bitcoin. Currently, if we don't have a healthy number of nodes that have both clearnet and tor peers, it is possible for an attacker to try to isolate the two networks from each other. Does the utreexo scheme create a similar concern?
Utreexo's design is driven by the need for Bridge Nodes: nodes that maintain backward compatibility with existing Bitcoin nodes and wallets that do not use Utreexo. A bridge node must be able to generate an inclusion proof for any UTXO at any time, with low latency, to support lightweight clients and peer nodes.
I did a bit of digging and couldn't find a really killer explanation of utreexo anywhere. This recent Bitcoin OpTech podcast had one of the BIP authors on to talk about a utreexo project called Floresta and was probably the best explanation I've heard so far.
As far as the draft uxtreexo BIPs, there are three BIP drafts in the linked repo:
If you want to learn more about utreexo, check out the Bitcoin OpTech page for it, BitMex's blog, or the original paper