Invocation in literature is an appeal for help, usually to a muse or godlike figure.
In "Ode to Evening," the speaker appeals to "Eve," a chaste and reserved figure he refers to as a maiden and "votress," (member of a religious order) to "teach" him to be able to observe and understand the soft unfolding of evening. Eve is the personification of evening, and she acts as his muse, allowing the speaker the inspiration to describe this quieter time of day.
Evening is pictured as a woman who is accompanied by the elves, who sleep by day in flowers, as well as by nymphs, to a "car" or chariot in which she will ascend. The speaker imagines her leading him to a lake on which the last tints of sunlight gleam. He will watch under her protection as her "dusky veil" falls over the earth. He then asks her to be a "gentle influence" on him through all the seasons of the year.
The speaker wants evening, his muse, to open to him a way of seeing and being that is gentler and more imaginative than that of daylight. He doesn't simply want to describe this dusky scene when the light fades, but to be infused with its soft, mellow, dreamy, and creative spirit.