Orderly as used in the paragraph above means well-arranged and organized. It is an adjective that describes the manner or how the flowers were arranged.
The supporting details in the paragraph show that this is the right meaning. The mention of the careful and neat manner in which the flower was planted can help a reader deduce what the word means. This word can also be used as a noun to signify an attendant who works in a hospital or a soldier who takes orders.
