In botanical terms, monandrous simply means to have a single stamen.
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In orchids
A distinction between monandrous and other flowers is particularly relevant in the classification of orchids. The monandrous orchids form a clade consisting of the subfamilies Orchidoideae, Vanilloideae, and Epidendroideae. The other subfamilies, Apostasioideae and Cypripedioideae, have at least two stamens.
In animals
In animals, a monandrous system occurs when females have one mate at a time. For example, a female speckled wood butterfly will typically only mate once within her short lifetime. This is also common in certain bee species, like Bombus terrestris and Bombus pratorum, where a female will only mate with one male during her nuptial flight and use the sperm reserves for the rest of her life. This is also seen in a few species of stingless bees, like Plebeia remota, where the males will attempt to mate with the queen as she tries to leave the nest, but only one male will be successful in mating.