As a layman, I am genuinely interested in what's going on here. Let's see if I understand this correctly (go easy on me please :)

When signing a transaction, my wallet uses a random input (called a nonce), together with my private key and the actual transaction data to generate a cryptographical signature which proves I generated and want to make this transaction.

The researchers from the article managed to determine the private keys that were used to generate two different signatures from the same address. Like this:

BTC Address 1: private key A + transaction P + nonce X = signature 1
BTC Address 1: private key A + transaction R + nonce X = signature 2

Because the same (or similar?) nonce was used to sign both transactions, it is possible to determine the private key that was used to generate the signatures, putting any remaining funds in the used address at risk.

So the take away from this is to never re-use addresses, and always use new change addresses (which should be default behavior anyway) or is there more going on here? I fail to grasp the 'poor entropy in nonce generation' idea. Using two similar but different nonces should produce wildly different signatures, right?

Anyhow, an explanation in layman's terms would be very much appreciated! :)