Critical appreciation is analyzing a work to evaluate its contents and explain why it should be appreciated.
While it's easy to like something, showing a critical justification for your appreciation is somewhat more difficult. You have to look at the work from a literary standpoint and evaluate it from that perspective.
Consider "Sonnet 18" by Shakespeare. Saying that it's a beautiful poem isn't critical appreciation—it's simply appreciation.
On the other hand, examining the structure and context of the poem can help you move from mere appreciation to critical appreciation. First, examine the structure. "Sonnet 18" is written in iambic pentameter, which is characteristic of sonnets. Iambic pentameter means the poem has four quatrains and ends with a rhyming couplet.
Next, examine the content. Shakespeare's "Sonnet 18" is based on a metaphor. The speaker compares his love to a summer day, but then goes on to clarify that he doesn't possess the negative aspects of that summer day. At the end, he says that his love will get to live forever through his words—death will never be able to truly lay claim to him.
You could end your analysis by saying that Shakespeare successfully uses iambic pentameter to achieve the goal of the poem—to immortalize his love.
So critical appreciation requires you to look at a word and analyze it to explain your appreciation for it. Knowing literary terms and tropes can help you as you do so.