"blah blah blah Bloom blah blah taxonomies blah blah revised Bloom" ~ Every education lecturer you will ever meet.
Bloom's taxonomy is a way of categorising just how sophisticated the learning objectives are for your students. If you're setting a test, for instance, you'll often think:
"Hang on, self. What is it I actually want the kids to know at the end of the fortnight? What should I really expect them to do?"
So you make a list of things that the students need to be able to do (recite the trignometric laws, or read musical staff notation). But if you force students to spit back only what you've told them, in a boring test of rote recall and soul-sucking textbook exercises, then not only will they hate your class (and possibly you (and perhaps life)), but they won't actually learn how to apply the stuff.
So Benjamin Bloom breaks down these learning objectives into different types, from simple recall to creating new things and evaluating them. To teach well, you should generally try to cover all levels of the taxonomy. The cognitive domain gets the most attention -- here are some tasks for mathematics, and their very rough cognitive domain level:
"Learn to copy these formulae, exactly as they are printed in your textbook"
"I have three spherical oranges with a total surface area of 30cm2. What's the total volume?"
Any problem that requires breaking-down into components, and perhaps multiple areas of math, will require analysis.
"Develop a method of determining the slope of my front lawn."
"Explain why you chose your method from (5), and what is good and bad about it. How could it be improved?"
295 words for BrevityQuest12