The Jewish belief in angels goes as far back as the Book of Genesis, where we read about angels calling out to Abraham at the binding of Isaac, angels appearing in Jacob's dream, Jacob fighting with an angel, and many more accounts of angelic activity. Angels are then mentioned numerous times throughout the other books of the Torah, Prophets, and Scriptures.
According to Jewish tradition, an angel is a spiritual being and does not have any physical characteristics. The angelic descriptions provided by the prophets – such as wings, arms etc. – are anthropomorphic, referring to their spiritual abilities and tasks.
The first angels mentioned by name in the Bible are Gavriel (Gabriel) and Michael, in the Book of Daniel. In earlier books of the Torah, when people asked angels to disclose their names, they refused; such as in the abovementioned encounter of Jacob with the angel, and the story of the angel who appeared to Samson's parents in the Book of Judges. The Jerusalem Talmud comments that reference to angels by name only became common in the period following the return of the Jewish people to Israel in 348 BCE. In the Talmud and Kabbala many more angels are identified by name. Some other commonly known names of angels include Uriel, Reziel, Metatron, and Laila.
Maimonides explains that all angels fall under one of ten ranks. Namely: Chayot Hakodesh, Ophanim, Erelim, Chashmalim, Seraphim, Malachim, Elokim, Bene Elokim, Cheruvim, and Ishim. These ranks refer to the degree of the angel's comprehension of G‑d; some have a greater understanding of G‑d and His ways than others.
The Hebrew word for angel is "malach," which means messenger, for the angels are G‑d's messengers to perform various missions. Every angel is "programmed" to perform certain tasks; such as Michael who is dispatched on missions which are expressions of G‑d's kindness; Gavriel, who executes G‑d's severe judgments; and Rafael, whose responsibility it is to heal. Some angels are created for one specific task, and upon the task's completion cease to exist. According to the Zohar one of the angels' tasks is to transport our words of prayer and Torah-study before G‑d's throne.
Another type of angels are those that are created through the deeds of man. In the words of our Sages: "He who fulfills one mitzvah, acquires for himself one angel-advocate; he who commits one transgression, acquires against himself one angel-accuser." These are formed from the (intellectual and emotional) energy which one invests in the performance of a mitzvah, the study of Torah, or in prayer—or, conversely, energy applied in the execution of a sin.
According to some schools of thought, the term angel in Jewish literature can also refer to the rules of nature, which – though ostensibly "natural" powers – are also G‑dly endowed powers; His messengers that perform His will.
In our daily prayers we refer to the songs of praise which the angels sing before G‑d. The angels have "shifts," singing at designated times of day or night. The type of praise they sing reflects the particular angel's spiritual status. The angels' singing is alluded to in the abovementioned story of Jacob's fight with the angel, at the end of which the angel pleaded with Jacob to free him "for the dawn has risen." According to the Midrash, the angel's rush was because his shift to sing before G‑d had arrived. Similarly, according to the Midrash, when Moses spent forty days studying with G‑d, he knew what time of day it was based on the changing shifts of the angels' singing.
Assuming Human Form
There is some debate among the great Jewish philosophers whether the angels that the Torah describes as appearing actually assumed a visible physical form, or they appeared in the course of a spiritual vision or prophecy—in which the angels appeared as physical beings. According to all approaches, however, seeing an angel requires extra-sensory perception, as the bodies of the angels are not comprised of all the basic elements of a physical being.
Angels vs. Humans
Notwithstanding the great spiritual level of the angels, the holiness of the Jewish soul supersedes that of the angel. Only the Jewish soul has the ability to descend to this physical and corporeal world and refine and elevate it. For the human's divine soul is a "veritable piece of G‑d Above," a "piece" of the Creator; as opposed to the angels which are creations—albeit very holy ones.
This reflects itself in that fact that angels are one-dimensional: each angels has one specific form of Divine service. The human soul, on the other hand, serves G‑d in many different ways, expressing itself through love, awe, etc.
In the Tanya, Rabbi Schneur Zalman of Liadi writes that he heard from his masters that "if one angel were to stand in the presence of a gathering of ten Jews, even if there were no words of Torah [being discussed] between them, such a boundless and infinite terror and dread would then befall him on account of the Divine Presence that abides over them, that he would become utterly nullified!"
Furthermore, angels have no free-choice and are pre-programmed to serve G‑d, whereas the human is entrusted with the mission of serving G‑d—but is given the freedom to choose to do otherwise. As such, the mitzvot performed by the human are of much greater value than the angels' service, and propel him or her to infinitely greater spiritual heights, as opposed to the angels who are "trapped" in a consistent level of spiritual consciousness.
Rabbi Sholom DovBer of Lubavitch once described the feelings he experienced while reciting the daily morning prayers: "When I recite the part of prayer which describes the praise that the angels sing before G‑d, I envy them. But when I read the Shema, the praise that the Jew sings before G‑d, I wonder: 'Where have all the angels gone?'"