HLT= hot liquor tank brewing water is called liquor during the process it is where you will heat your mash and sparge water for all grain brewing
MLT-This is the mashtun this is where you will add water and grain and get sweet wort out of it that will turn into hopefully turn into great beer
RIMS-recirulation infusion mash system. It relies on a tube with a heating element in it to heat the wort as it is recirulated through the tube and back to the mash. There is much more to it but that's the basics.
HERMS-Heat Exchanged Recirculating Mash System It basically moves the wort through a coil that is submerged in a liquid to maintain your mash temps. Again a very basic description
YFAGH-?
Single tier refers to the fact that all of the vessels are on one plain usually requiring a pump to move liquid throughout. Two tier usually uses gravity to transfer at some point and still could require a pump. Three tier relies on gravity to move everything around.