It is often difficult to understand what a teacher means when they ask you to write analytically or they put comments on your essay that say "Analyze this in more detail!" or, even less helpfully, just "Analysis?" Here is a good example of how analytical writing differs from other kinds of writing which will hopefully make it clear what I want when I ask you to analyze a text. All of the examples are based on the text  Jane Eyre  by Charlotte Bronte, which we have not studied, but the key differences between the different levels of writing should still be apparent.
There are four basic levels in writing about literature:
Description
Commentary
Discussion
Analysis
Level 1: Description
The following quotation illustrates  descriptive  writing:
‘ … Jane is mistreated by the Reed family, and although she is solely dependent on them to secure her livelihood, she speaks out against her harsh treatment…'
This is clearly just describing what happens in the text. Descriptive writing tends to simply retell the story and stick to the sequential order of events in the plot. In essay work, description of this kind is basically of a limited value and can never secure a high grade. It does demonstrate that the novel has been read but gives no indication of whether anything has been understood about the significance of the events depicted.
Level 2: Commentary  
The next quotation begins in the same way but progresses further. It is an example of  commentary  writing.
‘ … Jane is mistreated by the Reed family, and although she is solely dependent on them to secure her livelihood, she speaks out against her harsh treatment.  This shows that Jane is becoming something which society disapproves of - a woman with a voice and opinions of her own  …'
Here, we have moved from description to commentary. The factual description is supplemented by comments on the significance of events. This is where you start to gain marks - but the above commentary is still limited. If the essay continues in this way, citing incidents and attributing significance, then it would disintegrate into a long list of events, with none examined closely. Therefore, it is at this point that you must progress into the third level.
Level 3: Discussion
Discussion is a developed treatment of one single event in the text.
‘… When she protests against her treatment by the Reeds, Jane, of course, engages in a laudable act of rebellion and self-assertion. But the emphasis of the passage is not really upon this but upon the heroine's realization of her own powers which are tested in this episode for the first time. ‘What strength had I to dart retaliation at my antagonist?' she begins by asking herself. When she makes her verbal assault ‘I gathered my energies and launched them in this blunt sentence', she is herself shocked at the force of her own words as Mrs. Reed is silenced and rebuffed ‘Mrs. Reed looked frightened ... she was lifting up her hands … and even twisting her face as if she would cry' …'
Here the essay has moved from commentary, which is essentially a series of more or less isolated points on events in the book, to discussion. This is a sequence of points linked together and having a single focus.
The preceding quotation concerns one aspect of the scene, which is Jane's sense of the force of her own personality. There is an underlying meaning which the essay has picked out and highlighted:
If Jane had stated in the text she was shocked at the force of her words, this would be  descriptive . However, she does not, and so the essay writer has had to work this out for themselves which takes this beyond the level of description.
If the essay praised or blamed her for her assertiveness or told us why it was important then this would have been  commentary  and part of a catalogue of events which are listed and either approved or disapproved of.
Instead, what makes this  discussion  is that it picks up on a less obvious aspect of the text and then explores and writes about its implications in greater detail.
Commentary can