Exact Word Match Example
var search_word = 'me';
var arr = ['help','me','please'];
arr.filter(function(el){return el === search_word}).length;
The filter function will return the element if the result of the function is true. The function is called on each element of the array. In this case, we are comparing the array element to our search word. If they are equal (true) the element is returned. We end up with an array of all the matches. Using .length simply gives us the number of items in the resulting array; effectively, a count.
Partial Match Example
If you were to want something a little more robust, for instance count the number of words that contain the letter l, then you could tokenize the string and scan the index, or use some regex which is a little more costly, but also more robust:
var search_word = 'l';
var arr = ['help','me','please'];
arr.filter( function(el){ return ( el.match(search_word) || [] ).length }).length;
Note that match also returns an array of matching elements, but an unsuccessful match returns undefined and not an empty array, which would be preferred. We need an array to use .length (the inside one), otherwise it would result in an error, so we add in the || [] to satisfy the case when no matches are found.