How come astronomers can look at the sun through telescopes but can't look at the sun directly

It says "New German telescope stares at the sun"

Isn't it worse for your eyes that way?

The only safe way to look at the Sun is with a suitable filter, a sheet of glass or plastic coated with metal which reflects away 99.9% of the Sun's light and heat. Such filters are readily available from telescope stores, and are placed in front of the telescope, so that the dangerous radiation is reflected away harmlessly. I have filters like this for most of my telescopes.

[Edit] I assume you were referring to this article:
http://lightyears.blogs.cnn.com/2012/05/…
This is without a doubt the most brain-dead stupid astronomy article I have ever read in my life. I'm amazed CNN actually pays people to write crap like this.

As described in other responses, astronomers can use filters to prevent damage to the telescope and to themselves. A filter is an optical element that is installed - usually on the front of the telescope - that reduces the amount of light passing through it by a significant amount. Some filters also limit by frequency, which allows the observer to see details on the solar "surface" like flares and thermal cells easily. Without such a filter, a telescope - and your eye - will rapidly be damaged by the intense amount of solar radiation that is concentrated by the telescope.

If it's a telescope specifically designed for observing the sun, it will be designed very differently to a regular one you look through. It may have sensors that only pick up specific wavelengths, for example.
And btw it's NOT the UV light that burns your eye out, it's the far infrared (heat radiation) that will do it. Though also the UV and visible will damage the retina too along with it.

Filters remove the majority of the intense energy coming from the sun, before it enters the telescope and your eyes.