What is it that angels do in heaven?
There are different types of angels, as we were taught. And the question of what they do depends on what types of angels they are. Some interpretations of the Sepher Yetzirah tells us that some angels were actually "agents" of creation, each representing the different stages of creation ("stages" were , of course, just based on our perception), thus, it was written:
כו וַיֹּאמֶר אֱלֹהִים, נַעֲשֶׂה אָדָם בְּצַלְמֵנוּ כִּדְמוּתֵנוּ; וְיִרְדּוּ בִדְגַת הַיָּם וּבְעוֹף הַשָּׁמַיִם, וּבַבְּהֵמָה וּבְכָל-הָאָרֶץ, וּבְכָל-הָרֶמֶשׂ, הָרֹמֵשׂ עַל-הָאָרֶץ.
Some were warriors. Some messengers. Some were "administering" beings in heaven paying tribute day and night, forever.
Taken from here:
The Talmud (Chulin 91b) examines the angels' Divine service and concludes, "There exist three categories of angels who sing G-d's praise. The first group exclaims the blessing 'Holy' once. A second assembly praises G-d twice, 'Holy, holy.' And the third set repeats the acclaim three times, 'Holy, holy, holy is the L-rd of hosts'."
The Talmud there discusses other aspects of the Angels' songs, including frequency and that they have to wait for the Jews to sing praises before they can (which brings to mind this story told by the Ba'al Shem Tov).
The concept of the Angels and Heaven is extremely esoteric, and the prophecies which relate first hand visions of Heaven are not to be taken literally, namely Ezekiel and Isaiah. Rambam defines many of the words used in the accounts, and how they should be properly translated in order to understand it. He teaches that the angels are strongly interwoven with "God's Glory", the creation, chaos and the natural-laws of the universe, what he calls "divine science". It's not really supposed to be discussed as it can be very easily misunderstood, however, in The Guide of the Perplexed, the Rambam does his best to explain it without violating the prohibition.
God is incorporeal and unchanging, as such He uses messengers to interact with lower worlds that require physical-interaction.
Angels don't have free will the way man does and they have to follow Hashem's will. There is a bit of leeway in how they can fill God's command, but ultimately there is a governing-command that they must follow. In nature, it is similar to how a leaf floats down from a tree, it will definitely fall to the ground but how it gets there is unpredictable.