There are several factors to this practice. I'll try to list them and give a decently clear picture how it worked.

1. During the Victorian era, a lot of tradition carried over from earlier era, and uniforms were a part of that.

2. Despite what you might think, uniforms in the field were actually often quite practical. You see paintings and pictures of ideal uniforms in parade conditions. Parade uniforms were washed, and designed to look smart rather than be comfortable. In reality, troops usually had a field coat and a parade coat.

3. Light units and colonial forces started wearing colours to blend in more. British troops in India started wearing khaki (or rather tan) uniforms in the 1850s. Light troops were often wearing more practical green, grey or tan uniforms from the late 1700s and onwards.

4. With the usage of black powder, a battlefield would quickly be covered in smoke. A unit that did not keep together and could not be commanded by the army's leadership was useless, or even worse than useless - counter-productive, since it would draw rations and use ammunition but not contribute. Units moved together and fought together in close ranks, or they would be destroyed and scatterted by enemy charges by cavalry or infantry. Before the introduction of the repeating rifle, salvo fire by tightly packed men were the best way to deliver damage to the enemy. Having brighly coloured uniforms allowed you and your leadership to see your unit, keep it together and command it in the smoke.

5. Before the national conscriptions that happened in the Napoleonic war, armies were usually proffessional. In order to attract officers and men, you offered them to look smart. No-one wanted to look like a peasant in undyed clothes when elisting.

6. High hats and bear hats protected somewhat against cuts from above from cavalry swords. It also made a line of men look taller, stronger and more intimidating.

As always, not to discourage other answers, but his question was answered to a large part in depth a few days ago.