I was just looking this up in my several Japanese dictionaries but could not find the kanji, 寿司 , which is the most common form.
Looking online, I find the explanation that this is just a fancy phonetic form, SU SHI, or すし in the phonetic hiragana syllabary, and without a semantic basis, except the first character has propitious intimations of good luck, etc. so it is essentially a marketing creation.
The kanji, 鮨 , has the meaning of "delicious fish".