Know number of checkboxes selected

This is the code you need:

$('input[type=checkbox]:checked').length

If you want to run every time one is changed you can use it like this:

$('input[type=checkbox]').on('change', function () {
    var total = $('input[type=checkbox]:checked').length;
    alert(total);
});

Example: link Documentation: link

I'll leave a suggestion for implementation

HTML

<label><input type="checkbox" name="ch" /> Opção</label>
<label><input type="checkbox" name="ch" /> Opção</label>
<label><input type="checkbox" name="ch" /> Opção</label>
<label><input type="checkbox" name="ch" /> Opção</label>
<label><input type="checkbox" name="ch" /> Opção</label>

<div id="contador" data-value="0">

</div>

CSS

label {display:block;}
#contador[data-value="0"]{
    display:none; /*oculta qdo não houver nenhum selecionado*/
}

jQuery

$('input[type=checkbox]').on('change', function () {
    //quantidade de selecionados
    var qt = $('input[type=checkbox]:checked').length;   
    //coloca o atributo para ocultar qdo for 0
    $('#contador').attr('data-value',qt);
    //coloca o resultado na div contador
    $('#contador').text(qt + (qt > 1 ? ' selecionados' : ' selecionado'));
});

JSFiddle

Html

<input type="checkbox" name="check1" value="1">
<input type="checkbox" name="check1" value="2">
<input type="checkbox" name="check1" value="3">
<input type="checkbox" name="check1" value="4">
<input type="checkbox" name="check1" value="5">    
<div id="checkcount"></div>

Script (Javascript)

var contador = function() {
  var n = $("input:checked").length;
  $("#checkcount").text( n + (n === 1 ? " é" : " são") + " selecionados" );
};
contador(); 
$( "input[type=checkbox]" ).on( "click",contador);

Example: JsFiddle >

Reference:

• : checked Selector

A simple way to do this is through the new jQuery property, so you need to add a "key" class in your checkboxes to be able to do the verification:

$('.checkbox').prop('checked', true);
$('.checkbox').prop('checked', false);

With CSS counters you can " define a variable "to be incremented whenever a rule gets married. In case, how do you want to count how many <input> are with the :checked true attribute, just:

input:checked {
  counter-increment: checked-inputs
}

h2::after {
  content: 'Itens marcados: ' counter(checked-inputs)
}

<input type='checkbox'>
<input type='checkbox'>
<input type='checkbox'>
<input type='checkbox'>

<h2></h2>

input {
  counter-increment: total-items
}

input:checked {
  counter-increment: checked-items total-items
}

h2::after {
  content: counter(checked-items) ' de ' counter(total-items)
}

<input type='checkbox'>
<input type='checkbox'>
<input type='checkbox'>
<input type='checkbox'>
<input type='checkbox'>
<input type='checkbox'>
<input type='checkbox'>
<input type='checkbox'>

<h2></h2>