To comprehend is to 1) to grasp the nature, significance, or meaning of; 2) to contain or hold within a total scope, significance, or amount; or 3) to include by construction or implication.
To understand is to 1) to grasp the meaning of; 2) to grasp the reasonableness of; or 3) to have thorough or technical acquaintance with or expertness in the practice of.
Although the words have similar meanings, they have two different language origins. Comprehend is from the Latin word comprehendere, meaning to grasp. Understand is from the Old English word understandan, which means to stand.
There is an assumed difference between understand and comprehend. In society, most people believe that to comprehend a subject means that you have a greater understanding than just the basic information. Based on the definitions, this presumed difference is simply a societal understanding of the words.