Apsaraa is considered the female counterpart of Gandharv. All Apsaraa connote beauty. Normally they entertain Devtaa and fallen heroes in Indra's court. Indra also uses them sometimes for his work - to disturb sages' penance. His most famous uses of Apsaraa to disturb the sages' penance are --
(1) to send Urvashee to disturb Vishwaamitra's penance,
(2) to send Menakaa to disturb Vishwaamitra's penance - resulted in the birth of a girl Shakuntalaa,
(3) to send Janapadee to Sharadwaan Rishi - resulted in the birth of Kripaa and Kripee
(4) to send Pramlochaa to Kandu Muni - resulted in the birth of a girl Maarishaa.
In the Rig Ved and Atharv Ved also the Apsaraa are said to be connected with water and compared to swans or ducks (Rig Ved, 10.95.9 etc.). This seems to be logical as they had come out of the sea.
In Mahaabhaarat, Shakuntalaa reminds Dushyant, that "there are only six foremost Apsaraa - Urvashee, Poorvchitti, Sahajanya, Menakaa, Vishwaachee and Ghritaachee. Since Menakaa was born from Brahmaa Jee, she is the first and foremost one."
But there is only one Apsaraa, Urvashee, who is mentioned in only one Ved, that is Rig Ved (Book 10, Hymn 95). She married Chandramaa's grandson Pururavaa and had 6 sons from him. Chandramaa's son was Budh from Brihaspati's wife Mamataa, and Budh's son was Pururavaa from Manu's daughter Ilaa and that is how Chandra Vansh started on Prithvi.
It is said about Urvashee that -- Once Naaraayan and Nar, the sons of Dharm, were doing penance in Badaree forest. Seeing their penance Indra got afraid, so he sent some Apsaraa to disturb their penance. When they came at the place where Naaraayan and Nar were there, Naaraayan scratched His thigh which produced a very beautiful Apsaraa (Urvashee) seeing whom all Apsaraa got embarrassed and went away from there. Later Naaraayan gave Urvashee to Indra. That is why Urvashee was the most beautiful Apsaraa of Indra's court and he regarded her very much.
In Vaayu Puraan (13.69.51) and in Vaaman Puraan (7.1-45-5) it is mentioned that Urvashee was born from the thigh of Naaraayan. In Mahaabhaarat. Urvashee's other name is Gangaa.
So it seems that Urvashee and Menakaa did not come out of the sea. One was produced by Naaraayan himself and the other one was produced by Brahmaa Jee.
I still do not understand how Apsaraa word, and especially Urvashee, is mentioned in Rig Ved and it is connected to water, because Urvashee has been born from the thigh of an incarnation of Vishnu, and no incarnation is mentioned in Ved, then how an Apsaraa can be mentioned?