How do I understand this description of lumber?
Technically, the 1x8 is 3/4" THICK, not "high". That's nitpicking, though. A 1x8 is always specified as a "1x8", never by actual stock thickness in softwoods (ie pine). A nominal 1" plank will always be 3/4" thick after planing, a nominal 2" plank will always be 1-1/2" thick after planing. Width is a little different, but follows generally the same rules - an "N"x2 is always 1-1/2" wide, an "N"x4 is 3-1/2" wide, an "N"x6 is 5-1/2" wide, BUT an "N"x8 is only 7-1/4" wide. Wider planks than nominal 6" are narrower by 3/4" instead of 1/2".

The "5/4" (pronounced "five-quarters") is correct, very commonly used for hardwoods and occasionally for "presentation grade" softwoods. That's a plank that begins life rough-sawn at 1-1/4" (5/4") thickness and is planed to 1" thickness.

"Clear" - no knots or bark inclusions.