Comparison in writing discusses elements that are similar, while contrast in writing discusses elements that are different. A compare-and-contrast essay, then, analyzes two subjects by comparing them, contrasting them, or both.
Comparing involves identifying similarities and/or differences (e.g., apples and oranges are both fruit) whereas contrasting involves comparing two or more objects or events in order to show their differences (e.g., an apple has a thin skin that we can eat; an orange has a thick skin that we cannot eat).
A comparison-contrast paragraph has three main parts. The topic sentence introduces two subjects and says something about them. The body sentences give details about how the two subjects are alike and different. The ending sentence sums up how the subjects are the same or different.
Example of compare-and-contrast: you wouldn't compare/contrast reading a book to driving a car, but you would compare reading a book to reading with an e-reader.