Telescopes have been around a lot longer than the 19th century. However there are a couple signifigant events that happened to help improve the quality of the telescope during the 19th century.
First, the art of glass making improved. The purity in optical glass was important for the quality of the lenses. This became an important factor with the development of refractor telescope. The blurirng of colors by lenses (chromatic aberration) was also a huge step forward in the improvement of the telescope.
Here is a link to a detailed overview of the history of the refractors if you wish to read further on it.
Below are two images 19th century telescopes.
This is a Morgan hand held telescope. What you might picture in your mind's eye of being used by sea captains on board ships.
This is brass refractor telescope that sets on a stand. Note the various lenses at the base of the stand allowing the viewer different magnifications.