Anesthesia is a misspelling, principally used by lazy and/or ignorant Americans, of anaesthesia. We say lazy, but if we weren’t so worried about being tagged as an adult site we’d include a swear word before lazy to provide the proper emphasis. Really. How lazy do you have to be to intentionally exclude a single letter just for expediency’s sake?
As you will know if you read the definition when it was originally posted or you summoned up sufficient energy to click on the link we provided in the previous paragraphs, you’ll already know the definition anaesthesia and, hence, the misspelling of the word, i.e., anesthesia. Because you and everyone else is probably far too lazy for that, we’ll simply say that anaesthesia is an archetype of a character that appears in many Russian novels.
If you want to know any more than that then stop being so frigging lazy. Click the link and read it. We’re not going to do everything for you.
Because it’s a misspelling and not a legitimate word, by rights, anesthesia shouldn’t appear in the dictionary at all. However, many dictionaries include it because they feel the mercenary need to cater to lazy and/or ignorant Americans. This is particularly true of online dictionaries, such as this one, that hope to garner some search traffic off that misspelling.