Here's an attempt for ELI5. Well maybe more like ELI12.

NUD works on two fronts. First you need to have a Tor address.
(You need to install Tor yourself and turn your wallet into a hidden service)

Others on the network will not then see your IP address, instead
they see you something like lcqnp3bufy2hoosd.onion.

When your  address is relayed through Tor network, it's pretty good anonymity,
meaning that it is pretty hard for anybody figure out who is behind
the .onion address.

This in itself is not very remarkable (some other coins have it too), but NUD
adds another layer of anonymity in the form of transactions by delegate.

A delegate is someone who uses a part of his total balance to service
other users for a fee. So when you want to send NUD anonymously,
your wallet contacts a delegate wallet that has enough NUD to fund
your transaction. Then the delegate transfers his coins to recipient,
and afterwards you send an equal amount (plus delegate fee) to the delegate.

The end result is that there is no record in the blockchain that links you to the recipient.
What is recorded are the payments from the delegate to the recipient
and from you to the delegate, but for an outsider it is hard to say who is the sender
and who is the delegate, especially when there are many transactions
of this kind.

The wonderful thing is that all this happens kind of automatically. The
sender just pushes a button and goes to sleep. The delegate can be
asleep all the time. The wallet takes care of the processing. And if something
goes wrong (like computer crashing when they're asleep), the sender or the delegate can
reclaim their NUD. That works because the transactions have an inbuilt escrow
mechanism.

This is the gist of it. In practice however there are still a few hurdles and
wrinkles, that will no doubt be levelled out as NUD matures.