Outside of the gift of a red rose — which has been commercialized and commodified extensively — there are few flowers today whose meanings are widely recognized outside of hobbyist circles or florists. Now, the language of flowers, or floriography, has primarily been relegated to a secondary visual language used (both deftly and clumsily) in art.
In Victorian England, myriad factors led to the development of flowers as a way to send emotionally-charged messages meaning everything from love to sexual desire to hatred. The Victorian Era was one of industrial progress, leading to a rising middle class and more widely-available leisure activities. Victorian morality is commonly described as draconian or puritanical. The reality is a bit more complex. For example, alongside the rise of the novel came the rise of erotica and the expression of sexual desire in written letters. Floriography accompanied this. Through flowers, people could send coded messages to each other — some that they could even wear as fashion accessories — that said what they could not speak aloud due to the morality of the time. As western floriography developed through the Victorian era, so did the varied meanings that could be expressed. One flower could mean something when paired with another flower, and carry an opposing meaning when paired with a different flower. Floriography and the written word also merged together well, with novels of the time period referencing flower language with the expectation that readers would parse their meanings.
Violet Evergarden plays with a Victorian aesthetic and steampunk-like anachronism (which is why discussing Victorian floriography is more appropriate in this case than the iconography or different meanings of Japanese hanakotoba, prevalent in other anime).