JavaScript template engines are often used when writing thick JS-clients or as “normal” template engines when using server-side js like Node.js.
Instead of cluttering the code by generating HTML using string concatenating etc., you instead use a template and interpolate the variable in them.
For instance in the example bellow you pass in an array foo to the template engine which then interpolates (replaces the placeholder ${data}) with item i from the array foo:
//pseudo code
<table>
<tr>
for each variable data in foo
<td>${data}</td>
end
<tr>
</table>
In frameworks like backbone.js you typically use a template to implement the view part of the MVC pattern.
There are many different types of template engines in JS. Some are direct ports of server-side frameworks like ERB, HAML etc. Others are developed specially to work with JavaScript i.e Pure
There is a debate of how much expressiveness the template engine should give you because putting logic in your templates is usually a bad thing. Because of this some template engines are specifically designed to not let you put logic in them i.e Mustache