Which part of human eyes is getting tired?
These symptoms have a name: Computer vision syndrome.
Basically our eyes are made to look at longer distances from 1-6 meters without much accommodation. Typically computer screens are located at a much closer distance (30-50cm), which requires constant accommodation by the eye. This leads to high stress on the muscles in the eye which subsequently get tired. Additionally less blinking leads to drier eyes.

One of the common recommendations against this is to regularly focus further located objects to give the eye the chance to relax. This is sometimes called the "20-20-20" rule, every 20 min focus on a 20 feet (about 6 m) far object for 20 seconds. See the article in the Wikipedia and here for more information (and probably also the linked references in the articles).