Many scientific experiments have been carried out on the shuttle, but it has also been used to transport astronauts on missions to repair broken satellites. Humans are still better at fixing things than robots.
The Solar Maximum Mission (SMM) was launched in February 1980 to study the Sun when it was very active. The satellite worked for almost a year and then one of the components broke. The only way to fix it was to use the shuttle. In April 1984, the space shuttle Challenger was launched to repair SMM. The astronauts used a long arm on the space shuttle to capture SMM and bring it into the cargo bay, where it could be fixed . They then put SMM back into its orbit and it worked well for another five years.
Here is an eruption (coronal mass ejection) seen by the coronograph on SMM
The Hubble Space Telescope (HST) was launched by the shuttle in April 1990. It should have had a really clear view of the stars, but instead its vision was blurred and everyone was really disappointed. The problem was that its mirror had been made very slightly out of shape. So in 1993, the shuttle captured HST into its cargo bay and the crew went to work fixing the telescope. They fitted some specially designed spectacles so that HST would have the perfect 20:20 vision. Since then HST has provided a spectacular view of the heavens.