As its name suggests document.getElementsByClassName returns a list of elements, with the hover as their className, so you can do it like:
var i=0,
  len = abbrs.length,
  abbrs = document.getElementsByClassName("hover");
for( ; i < len ; i++){
    abbrs[i].addEventListener("mouseover", function(event){
        //...
    });
}
Although it answers the question but in terms of a better coding practice we better avoid from creating functions in loops. So the better practice could be something like this:
var i=0,
  len = abbrs.length,
  abbrs = document.getElementsByClassName("hover");
fnction addEvent(abbr){
    abbr.addEventListener("mouseover", function(event){
        //...
    });
}
for( ; i < len ; i++){
    addEvent(abbrs[i]);
}