Great question, I'm surprised nobody else answered. Noticed you asked twice as well. I think there was a question about the Aten in the Egypt AMA a while ago so you might want to check that out.

The Aten was originally a fairly unimportant aspect of Re, the sun god. It is really the physical aspect, that which can be seen. It became prominent in the reign of Amenhotep III and Akhenaten. As a bit of background, Thebes was the most important city at the start of Amenhotep's reign, so Amun, being the god of Thebes, was most prominent. As Amun had became the most prominent, he was melded into a form with the sun god Re and became Amun-Re.

This probably all started with Amenhotep III, father to Akhenaten. Akhenaten was born Amenhotep IV. The symbol of the Aten was used by Amenhotep III towards the end of his reign. Some historians dispute this, saying that Amenhotep was never worshipped as the Aten in his lifetime, and this was more of a retrospective deification by his son. There is also some dispute about whether they ruled together, but that's not particularly relevant so I'll leave that aside.

The cult of Aten was somewhat of a church and state issue. Akhenaten was trying to counteract the growing power of the priests at the Karnak temple in the capital Thebes and the powerful, popular god Amun-Re. The priests had control over vast resources and the king faced a constant power struggle against their influence. To curb the power of the temple, Akhenaten began to venerate the Aten at the expense of the other gods, building a temple of Aten which encroached on the temple of Amun.

So in Thebes there was social and political upheaval because the people didn't want to give up their favourite god. There were conflicts with Amun-Re priests, who continued to use their influence in the capital. Rather than deal with it there (it was probably too far difficult to bother), Akhy decided to just move his court to Akhetaten (Amarna) (Axt-itn 'horizon of the Aten') where he was free from the influence of the temple of Karnak.

In doing so, he took the Aten as his symbol, and created a monotheistic religion, considered heretical at the time. It was not easily accepted, especially by the common folk. It should be added that Akhenaten didn't do away with other gods entirely, such as the Ma'at (truth, order) and Hapi (the Nile flood), which came to stand more for concepts rather than embodiments of gods as they had previously. In saying that, these were also considered concepts as well, not just in the Amarna period. Ma'at for example, was considered a way of life.

Whether or not he or his father truly believed in the Aten, Akhenaten seemed pretty keen on it. Check out the Great Hymn to the Aten, attributed to Akhenaten, which is some beautiful, ostensibly heartfelt poetry considering he's talking about a sun disc. Some scholars do think rather than true devoutness, Akhenaten meant to combine divinity and kingship more tightly for politically expediency. I like Assmann's suggestion that it is a way to simplify a complex polytheistic crisis where god was basically unknowable as there were so many forms. It's hard to say which of these is correct or whether a dichotomy is even needed. There may be a rich tapestry inspiring Akhenaten's adoption of the Aten, woven with both political and theological threads.

Anyway, here's a little bit of the Hymn. My translation is a bit rough but you get the idea that he's a big fan of the Aten:

xay.k nfr m Axt nt pt

itn anx SAa anx

iw.k wbn.ti m Axt

mH.n.k tA nb m nfrw.k

iw.k an.ti wr.ti THn.ti qA.ti Hr-tp tA nb

stwt.k inH.sn tAw r r-a irt.n.k nb

iw.k m ra in.k r r-a.sn

waf.k sn (n) sA-mr.k

iw.k wA.ti stwt.k Hr tA

tw.k m Hr.sn nw Smw.k

You rise beautiful in the horizon of the sky,

Aten of life, origin of life,

you are arisen from the horizon,

you have (filled) all lands in your goodness,

you are fine, great, brilliant, high above every land,

your rays enclose the lands in the entirety of what you have made,

You are (in a state of being) the sun, you reach their limits,

You bind them for your beloved son,

You are far away, but your rays are on the earth,

They see you, but hidden are your movements.

Now, the artistic revolution in the Amarna period is so incredible that it's hard to fathom that some pieces that originated there were even Egyptian. It seems more in line with European art movements. Much of this traditional style is tied up in the religiously and royally prescribed artistic conventions. Free of influence of old gods, Akhenaten threw out all of these old rules and that's why you see such a revolution, often considered to be a type of artistic naturalism.

This is misleading though. The elongation of features, or feminisation of the king's body tend to be reflective of idealism rather than realism. Studies of the remains in Tomb 55 in the Valley of the Kings, believed to be Akhenaten, have not shown evidence of the elongated physical depictions of the king (See Harrison). This was probably simply propaganda, a product of Akhenaten's religious monotheism (or perhaps more accurately monolatry: see Monserrat) and an attempt to create a style distinct from tradition. The artistic depictions of Akhenaten and his wife, Nefertiti, on the same level suggests they may have ruled together as equals. The feminised depictions of the king (and I'm speculating a bit here) may be related to a political and social acceptance of the feminine in a kind of reverse of Hatshepsut, rather than any realistic features.

But essentially, the reason for the vast differences in art of this period is that Akhenaten simply encouraged artists to go in new directions. Much of this divergence is a result of the artistic interests of the king combined with the importance of distinguishing cult of the Aten in the developing theology and philosophy of the time, as well as to establish the king as the sole political power. To answer your question more explicitly, the Amarna period's art revolution is brought about by a religious and political power struggle, differing theological ideas and the desire to explore and create cultural distinctions.

Some sources:

Dominic Monserrat, Akhenaten: History, Fantasy and Ancient Egypt

Jan Assmann, Egyptian Solar religion in the New Kingdom

L Harrison, An Anatomical Examination of the Pharaonic Remains Purported to Be Akhenaten

EDIT: formatting