It means constant or consistent effort, to deal with a task or many tasks. It means start somewhere and continue until you have finished. It usually means the way you make the effort is methodical, say you had a large pile of dirt (compost, earth) that you had to move from one place, to another place, you would have to work through it bit by bit. But "work through" in the context of instructional books, means to begin somewhere and continue. One of your examples said, "Don't work through the units in sequence" This means please do all of the work, complete the units, but please don't do them in order of 1, 2, 3, 4, 5 etc or ABCDEFG (chronological order). Is that ok?

The definition in your dictionary is a good one. This phrasal verb also suggests a formidable undertaking that might seem somewhat intimidating, but the verb also carries with it a certain confidence that a careful and methodical approach will succeed. It's a useful expression.