How can a galaxy in-between our view and the galaxy behind it have a 'lensing effect'? In this article, the author writes:


  This galaxy is so distant that it would have been invisible without the gravitational lensing effects of a large galaxy cluster called Abell 1689, located nearly 2.2 billion light years away in the constellation Virgo. The cluster’s enormous mass acts as a natural telescope by bending and amplifying light from objects behind it, like A1689-zD1.


To me this doesn't quite sound the same as what a telescope is doing. 

My question is: How can a galaxy in-between our view and the galaxy behind it have a 'lensing effect'?
It's called gravitational lensing. Here's a link to the wikipedia article on the subject: http://en.wikipedia.org/wiki/Gravitational_lens.
Gravity affects everything, including light. A massive object such as a star, a galaxy, or in this case, a cluster of galaxies, bends the path of photons that pass very close to the massive object. Bending light is the basis of the lenses in an optical telescope.
The behavior of a gravitational lens is different from that of an optical lens., but the end result is the same: Gravitational lenses enable astronomers to see more distant objects than they would without them. Gravitational lenses create multiple images of the remote objects behind the lens. Oftentimes these multiple images are in the form of streaks. See the below image of gravitational cluster Abell 1689, which is the cluster that let those astronomers see A1689-zD1.

(source: hubblesite.org)
The cluster magnified the remote galaxy A1689-zD1 by a factor of 9.3. Without that magnification, that remote galaxy would be invisible to current technology.