Every Theophany I post an icon of the feast often with some writings about the significance of the event, some hymnography, etc. Without fail I will receive an email or a comment asking,"Who are those people riding fish?" After much searching I've found a wonderful treatment of the topic from St. Paul’s Greek Orthodox Church in Saskatchewan. I recommend not only the below, but the entire article available here (PDF).
Theophany icons have quite a few elements shared by all who write them, but they also have many elements one might call "optional." Sometimes the sea creatures will be very prominent and other times not at all. Sometimes the axe is visible and sometimes there is no tree at all. Sometimes the angels hold implements for the Baptism and other times they do not. The list goes on - it is interesting to also see in the above mentioned document a list of unwelcome innovations best avoided. Again, it's not to be missed.
At the bottom of the icon, at the feet of the Saviour, often, in small dimensions, appear the shapes of two persons – a man and a woman. Both are with the back turned toward Christ and look astonished. The two shapes illustrate texts of the Old Covenant and are prefigurations of the Baptism: “The sea beheld and fled; Jordan turned back” (Psalm 113:3).
The male figure – a person immersed in the river watershed holding a vessel from which water is poured out, is an allegoric representation of the Jordan River. This person turns his face from Christ, being overtaken by astonishment, even dread, the reason as per liturgical texts being: “I saw naked Him whom none can see, and shuddered in fear”. The troparion explains the presence of this figure:
“The River Jordan was once turned back by the mantle of Elisha, when Elijah had been taken up, and the waters were divided hither and thither. And for him the watery path became dry, Truly as a type of baptism, whereby we cross the flowing stream of life. Christ hath appeared in the Jordan to sanctify the waters.” (Prefestal Troparion)
The female figure – a half clothed woman, with a crown on her head and a sceptre in her hand, rushing while riding on one or two fish – is an allegory of the sea and refers to one of the prefigurations of Baptism: the passing of the Hebrew people through the Red Sea.
In some icons Christ is represented standing on two stone blocks arranged as a cross (similar to the gates of hell from the icon of the Decent into Hell) under which there are snakes with their heads risen or sometimes even a dragon appears under His feet. Thus, in this way the icon portrays Christ’s victory over the powers of darkness (the devil and his angels) symbolized through the marine monsters – dragons, snakes, -on the run or crushed-, detail inspired from Psalm 73:14 “...You did crush the heads of the dragons in the water”.
“When You bowed Your head to the Forerunner, You crushed the heads of the dragons; And when You stood in the midst of the stream, You let Your light shine upon all creatures, That they might glorify You, Our Saviour, Who enlighten our souls!” (Lord I Call – Vespers of Theophany)
“The Lord refashions broken Adam in the streams of the Jordan. And He smashes the heads of dragons lurking there. The Lord does this, the King of the ages; for He has been glorified.” (Vigil for the Theophany, First Canon)
Sometimes around Christ there are small fish, even children, but usually too many irrelevant details are to be avoided.
All these aquatic elements belong to the background in order to maintain the proper focus and convey the true understanding of the significance of the Feast.