The previous answer wrote great information about how the telescope is a changing piece of technology that has helped humans better understand astronomy and cosmology. From simple, small light collecting telescopes to the huge multi-mirror telescopes like the Keck, they have all helped humans see further into space and collect more information about the universe at large. As technology improved, so did our understanding of light. We realized that the human eye is only collecting a very, very small amount of the light frequencies that exist. In response, we invented telescopes that are able to collect wavelengths of light that we can't see. We now have telescopes that can see radio waves, microwaves, infrared, ultraviolet, x-ray, and even gamma radiation.
Technology has allowed astronomers to do more than just look through telescopes now. We have satellites in space closely monitoring the actions of our sun. The Solar and Heliospheric Observatory and the Solar Dynamics Observatory satellites are the two current leading satellites collecting solar data. They have been launched and placed at a Lagrange point between the Earth and the sun. That means the combined gravitational pull between the Earth the sun keeps the satellite locked in place, so the satellite gets a fully unobstructed view of the sun 24 hours per day. Astronomers have gained incredible amounts of knowledge about how stars work just from closely studying our own sun. Additionally, we now have the capability of monitoring and predicting how and when coronal mass ejections will affect earth.
My favorite use of astronomy technology is Gravity Probe B. Between 2004 and 2005, NASA monitored the associated satellite in order to determine if massive objects, like Earth, really do warp space-time. What they discovered was that yes, massive objects do bend space and time around them. The experiment allowed astronomers to verify previously untested parts of general relativity.