You can write onchange event for dropdown list and in javascript make an ajax call with the data i.e selected value to the method or service i.e the server.
Consider the following example,
HTML:
<select id="ddl" onchange="sendToServer()">
<option value="1">One</option>
<option value="2">Two</option>
<option value="3">Three</option>
<option value="4">Four</option>
</select>
JavaScript:
function sendToServer(){
var element = document.getElementById("ddl");
var selectedValue = element.options[element.selectedIndex].value;
$.ajax({
url : "put service/method url",
type : "post",
data : {value : selectedValue},
success : function(result){
},
error : function(xhr, status, error){
}
});
}