desert (v.) Look up desert at Dictionary.com
"to leave one's duty," late 14c., from Old French deserter (12c.) "leave," literally "undo or sever connection," from Late Latin desertare, frequentative of Latin deserere "to abandon, to leave, forsake, give up, leave in the lurch," from de- "undo" (see de-) + serere "join together, put in a row" (see series). Military sense is first recorded 1640s. Related: Deserted; deserting.
desert (n.1) Look up desert at Dictionary.com
"wasteland," early 13c., from Old French desert (12c.) "desert, wilderness, wasteland; destruction, ruin," from Late Latin desertum (source of Italian diserto, Old Provençal dezert, Spanish desierto), literally "thing abandoned" (used in Vulgate to translate "wilderness"), noun use of neuter past participle of Latin deserere "forsake" (see desert (v.)).

Sense of "waterless, treeless region" was in Middle English and gradually became the main meaning. Commonly spelled desart in 18c., which is not etymological but at least avoids confusion with the other two senses of the word. Classical Latin indicated this idea with deserta, plural of desertus.
Every important worker will report what life there is in him. It makes no odds into what seeming deserts the poet is born. Though all his neighbors pronounce it a Sahara, it will be a paradise to him; for the desert which we see is the result of the barrenness of our experience. [Thoreau, Journal, May 6, 1854]
desert (n.2) Look up desert at Dictionary.com
"suitable reward or punishment" (now usually plural and with just), c. 1300, from Old French deserte, noun use of past participle of deservir "be worthy to have," ultimately from Latin deservire "serve well" (see deserve).