Conjecture
This word is used as either a noun or verb, and in either case, suggests making a tentative judgment, based on partial evidence.  It is a statement of opinion with some basis in information, but The American Heritage Dictionary of the English Language* emphasizes the part that "guesswork" plays in making this statement of opinion.

Discuss
The second meaning, "To examine or consider (a subject) in speech or writing," given by The American Heritage Dictionary of the English Language*, is the most useful for the purpose of interpreting a writing assignment. To "examine" suggests that a thorough, close treatment of the subject is called for.
*4th edition, 2000, available online at www.bartleby.com

Respond
"To respond" means to communicate your reaction to a topic or text, including your feelings or ideas. Often, in the context of a writing assignment, it is expected that you will give reasons for your feelings and ideas as well as identify them.

Reflect
Reflecting means thoughtfully considering or meditating on a topic. The root meaning of "reflect" is "to bend back," and one meaning appropriate in interpreting writing assignments is "to think quietly and calmly." When "reflective writing" is assigned, what is suggested is a combination of calm, quiet thinking with a retrospective focus--looking back over a period of time and considering its meaning and significance in connection with your experience.

Compare
The strictly defined meaning of "compare" is to show similarities between two entities, but it is often used as a sort of shorthand for "compare and contrast," a pair of verbs that suggests to show both similarities and differences between two entities.

Contrast
"To contrast" means to show differences between two entities.

Explain
In a writing assignment, the meanings generally intended are these two: "1. To make plain or comprehensible. 2. To define; expound" (The American Heritage Dictionary of the English Language*). In some cases, however, the suggested meaning may be to give reasons for, as meanings 3a and 3b from the same dictionary indicate: "3a. To offer reasons for or a cause of; justify: explain an error. b. To offer reasons for the actions, beliefs, or remarks of (oneself)." The American Heritage Dictionary includes a discussion of several synonyms at this entry, part of which is reproduced here:

Illustrate
"To illustrate" means to use examples or comparison in order to explain or clarify a concept.

Inform
Informing implies sharing information. You may be asked to gather information in such a way that only you will have that information, for example, through direct observation. Once you've gathered your information, you will report it to others in a form that classifies and interprets it.

Classify
Classifying means arranging information into categories. In a writing assignment, these categories may be given by the instructor, or you may be asked to come up with appropriate categories.

Synthesize
Many research-based assignments ask you to synthesize information from several sources. When you synthesize, you must first analyze the information you've gathered and then organize it to make your own point or to serve the purpose of your particular paper. The American Heritage Dictionary of the English Language gives this meaning: "To combine so as to form a new, complex product."

Analyze
Once again, The American Heritage Dictionary of the English Language furnishes the best explanation of the verb: "To examine methodically by separating into parts and studying their interrelations." Note the emphasis on being methodical through looking carefully at the relationship between the parts of the topic being analyzed.

Interpret
"Interpret" is one of the synonyms listed for "explain," but the particularly significant aspect of "interpret" is to explain the significance of something, and this verb suggests that you take a critical perspective toward your topic (in the sense used in literary criticism or art criticism or music criticism).

Explicate
"Explicate" is another synonym listed for "explain." An explication, however, is a detailed explanation that analyzes as well as clarifies. The term "explicate" implies greater length and depth than the verb "explain" does.

Define
Defining means giving the precise meaning of a term or concept. Formal definition requires that the term be placed in a category and then distinguished from other terms in that category by the presentation of specific identifying features. For example, in the statement "Oligarchy is a form of government," form of government . . . is the category. The identifying features might be included in the rest of the defining sentence as follows: "where rule is concentrated in the hands of a few persons."

An extended definition might be a paragraph or even an essay in length. Such a definition might include examples, comparison/contrast with other related terms in the same category, and "negative definition"-- what the term does not mean. See Definitional Techniques by Prof. Merrill Whitburn at Rensselaer Polytechnic Institute's Writing Center for more information.

conjecture
discuss
respond
reflect
compare
contrast
explain
illustrate
inform
classify
synthesize
analyze
interpret
explicate
define

Other useful resources:

Taking In-Class Essay Exams, a handout from George Mason University Writing Center