The word nerf is an adapted word from the MMO community, much like the MMO community adapted the word "zerging" from "Zerg rush". The word itself refers to NERF-brand plasticized foam; a soft, spongey material designed specifically not to harm children. The MMO community adapted the word due to its associations with being 'safe' and 'harmless'.
In the context of the game, the word 'nerf' usually refers to changes in a patch where a class, race or other classification of the game has been lowered quality or efficiency. It could also mean that the price for something used has increased.
In some cases, "nerfed" can also refer to opponent components, such as a "boss" in an MMO.
For StarCraft, the term "nerfed" would be used if a unit got the production cost increased or their statistical numbers in terms of HP or damage lowered.
The opposite of nerfing is buffing.