"DX" is an abbreviation for "distance", generally used in the sense of "making long-distance contacts." A "QSO" is a successful contact between stations, and "working" refers to the process of making / attempting to make contacts.
"Multi-hop Es" refers to this atmospheric effect using the E region of the ionosphere: https://en.m.wikipedia.org/wiki/Sporadic_E_propagation
"CW" (for "continuous wave") typically refers to the use of Morse code over a constant frequency wave that's just being turned on and off, which has historically been one of the most robust modes, although it requires skill in encoding/decoding Morse by hand.
"73" means "best regards" or similar; it's from very old telegraphy abbreviations.
In a nutshell, Joe Taylor (K1JT) created a program that features novel modulation schemes that solve a few problems that other modulations didn't, like fast meteor scatter modes, modes that are better for Earth-Moon-Earth communications, and modes that work better in very low-signal scenarios with a lot of signal fading due to the ionosphere.
The result are modes that are very slow - only sending something like 13 characters every 15 seconds for FT8 - but far more reliable than other keyboard modes like PSK31 or Olivia. The mechanization means QSOs are stripped to their bare necessities - callsign, location, signal report, and that's it. It's shifts the idea of a QSO by forcing quick, scripted, nearly automated contacts, which is a very well-received change since a lot of HF ops are only interested in the contact, and not the person.
The basic mode only allows you to make contact, it doesn't allow for discussions or data transfer. It's simply a “I'm here, and I can hear you” mode.
It's controversial because a) to some hams, conversation is the reason to be on the air; and/or b) hams can be opinionated and grumpy, and some feel like if you haven't spent $5k on your radio/built your radio from scratch/exclusively use Morse code/devoted five acres of land to a 200 foot tall tower with a Yagi antenna you aren't doing it right. DX (long-distance communications) is an exclusive club. FT8 makes it a lot less exclusive. There's always resistance to that.