It would go too far to describe the entire history of gardening in the Nineteenth Century, so I’ll just give you some tidbits:
Wardian Case: The Wardian case was invented by Nathaniel Bagshaw Ward, in 1829. By accident he found out that his ferns grew very well in bottles, and he developed this idea to a larger case to hold full-grown flowers. This meant a great increase in the amount of flowers available in Europe. It became easier to import flowers because they were encased in a constant climate and did not suffer from the change of air and temperature while they were transported, and it was easier to keep exotic flowers alive during winter.
(Image from Wikipedia.)
Lawnmower: The lawnmower was invented in the first half of the Nineteenth Century, and was inproved quickly from a large and difficult machine to something that could be used by hand, by everybody. (Of course, women would not mow lawns.) The invention of the lawnmower caused a big rise in lawns in garden design around 1840, where before mostly flower arrangements and grit were fashionable.
Using flowers in interior design: Of course the Victorians were keen to find new ways to decorate the interior. Flowers were increasingly used in the Nineteenth century, not just as a bouquet but arranged as large ornaments. Here are some images from the book “The Victorian Flower Garden” by Jennifer Davies.
A popular pastime in the Nineteenth Century: an organized fern hunt. Found ferns could be added to ones fern collection, which was immensely popular.