Well, the JavaScript runs on the client and the servlet runs on your server. So you do need to send the value to your server somehow. The two (typical) ways to do so is using a form submit, or Ajax. Since you mention the value comes from a select box I assume you want to update something on the page when the user changes selection, using Ajax would probably be what you want.
Unless the amount of data needed to update is really large, likely to change often, or your intended client is really limited in bandwidth or computing power (like mobile devices), you may allso embed all the data needed on the page and selectively hide and show the data based on the selection without using a server call. If this is possible in your scenario it's more likely to feel fast and responsive than using Ajax.