Often, I skim most of the quantum stuff because the explanations trend heavily towards the technical and I don't see how spending a ton of time trying understand the math is really that useful for a layman like myself.

Still, it's nice to have a general sense of things, and here we have both @niftynei (the linked article) and @bitcoin_devs (#1064943, #1065841) giving us more accessible explanation of a new signature scheme proposed by roasbeef.

Tl;dr - quantum resistant signatures are bigger than the signatures currently used by Bitcoin. "A Segwit v1 Schnorr signature is 64-bytes of onchain data; comparable SPHINCS+ benchmark sigs are 3-7k bytes." But unlike some other hash based signature schemes, SPHINCS+ can safely sign multiple times.

The real reason I like nifty's article is that she does a great job of explaining some of the obstacles we are dealing with in developing and adopting a QR scheme.