Why does the Torah write "Machanayim," meaning two camps, when Yaakov met only one group of angels?
Rashi: It refers to the angels of Chutz la'Aretz, who were returning to Heaven, and those of Eretz Yisrael, who were coming to accompany him. 1
Ramban #1: It is a matter of style not to differentiate between singular and plural with regard to place-names.
Ramban #2, Ohr ha'Chayim: It refers to Yaakov's camp and that of the angels. 2
Moshav Zekenim: He saw two camps of angels, and thought that it is a Siman that he should divide into two camps. Really, it was a hint that the kingship of Yisrael would be divided into two in the days of Rechav'am, or that some Shevatim would inherit in Ever ha'Yarden.
Tosfos ha'Shalem (4, citing R. Efrayim): Machanayim is like Machaneh Yam, for each angel is like a sea 3 - "u'Geviyaso k'Sarsish" (Daniel 10:6).
Malbim: He saw that the angels are prepared for war, and understood that two camps will meet. This is why he sent messengers to Esav, for he knew that he is coming for war.
Since Tzadikim in this world are compared to angels. (EC)
Rashi (to Daniel 10:6): Each angel resembles Yam Tarshish (the Indian ocean), which is 2000 Parsa'os (about 8000 kilometers) wide.
How could Yaakov be calm when seeing angels?
Tosfos ha'Shalem (2): His sons were not used to seeing angels in Lavan's house. They feared that the angels are Esav's men coming to fight. Yaakov [who was used to seeing them in Yitzchak's house 1 ] assured them that they are angels; they are on our side.
Moshav Zekenim citing R. Yeshayah: He saw them in a dream. When he saw even one angel, he was astounded and said, "I saw Elohim face to face, and I was saved!" (32:31). 2
This is unlike Rashi (to 32:4, from Bereishis Rabah, and Moshav Zekenim himself) who says that Yaakov sent actual angels to Esav. We find that even Hagar saw angels, and was calm! Perhaps Yaakov was astounded at seeing one angel because he tried to kill him, or because that angel was the Sar of Esav, i.e. the Satan. (PF)
QUESTIONS ON RASHI
Rashi writes: "Machanayim - two camps...." How could both camps of angels be seen together? Gur Aryeh wrote above (to 28:12) that one camp of angels has to ascend before the other may descend, for two reigns never overlap?
Gur Aryeh (to 32:2) #1: Yaakov was still in Chutz la'Aretz. Although the angels of Eretz Yisrael had already descended, to protect him on his way and remove any obstacles, the angels of Chutz la'Aretz remained as well, to protect him from any other harm.
Gur Aryeh (to 32:2) #2: On this occasion, the first angels could not abandon Yaakov before the next ones came; doing so would leave Yaakov unprotected. 1