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What is Taro?
It looks to me like a new comm protocol for machines on the bitcoin network to describe more complex transactions than what's easily supported on BTC & LN already.
What is Taproot?
A change to way signatures are able to be included in on-chain transactions. These new signatures all look the same, irrespective of whether they are single or multi-signature. If i understand correctly, it supports multi-sig more rubustly. See here.
How does one relate to the other?
Taro is taking advantage of Taproot. Taproot doesn't relate to Taro.
Is this considered a "layer 3", since it purports to use lightning?
According to @kobie above, Taro can run on chain... which is whoa.
Anything else you can add for a simpleton.
I'm half-jokingly telling my friends to get ready for the real ICO boom as Taro would open up a bajillion cans of worms that (since they're settling to Bitcoin, instead of shitcoins) I suspect will be very interesting to hard-money enthusiasts who have been watching a lot of interesting, distributed, "defi" technology develop in the shit-coin space.
Good luck on your journey.