The words appreciate and comprehend are common synonyms of understand. While all three words mean "to have a clear or complete idea of," understand and comprehend are very often interchangeable, with understand sometimes stressing the fact of having attained a firm mental grasp of something.

// orders that were fully understood and promptly obeyed

The synonyms appreciate and understand are sometimes interchangeable, but appreciate implies a just evaluation or judgment of a thing's value or nature.

// failed to appreciate the risks involved

Although the words comprehend and understand have much in common, comprehend may stress the process of coming to grips with something intellectually.

// I have trouble comprehending your reasons for doing this