Genèse 1:20

"Living souls:" That has life in it.

"Swarming thing (sherets):" Every living thing that is not very high from the ground is called sherets: among flying creatures, such as flies; among insects, such as ants, beetles and worms; and among the [four legged] creatures, such as the weasel, the mouse, the lizard, and their like; and all of the fish.

And the Lord said, Let the lakes of the waters swarm forth the reptile, the living animal, and the fowl which flieth, whose nest is upon the earth; and let the way of the bird be upon the air of the expanse of the heavens.

"and He said, "let swarm" - this is a transitive verb, and similar to it: "The Nile swarmed [with] frogs" Exodus 7:28. The meaning is: Let swarm the offspring with [the ability of] elevation. And what is written - that the foul will fly over the face of the firmament - is witness for [my prior] explanation of firmament. Now the Ga'on has said that "on the face of" [here] is equivalent to "with [i.e., adjoining] the face". But if so, the face of the heavens are below. The [letter] feh of ye'ofef is doubled, like the non of yechonen.

LET THE WATERS SWARM WITH ‘SHERETZ’ (SWARMS) OF LIVING CREATURES. Rashi wrote: “Every living creature that does not rise much above the ground is called sheretz, [e.g., species] of winged creatures such as flies; of abominable creatures such as ants and worms; of larger creatures such as the mole and the mouse and others of the same kind, and all fishes.”
But what will the Rabbi say of the verse, And you, be ye fruitful, and multiply; ‘shirtzu’ (swarm) in the earth and multiply therein, which was said to Noah and his sons? Likewise, the verse stating, which ‘hamayim’ (the waters) swarmed, should, according to this opinion of Rashi, read: “Which swarmed bamayim (in the waters).” the waters. Again there are many winged creatures that do not rise in height above the ground even as much as the mole and mouse, and the bat has very small legs, so why should it not be called sheretz ha’oph (a winged swarming thing)?
Onkelos’ opinion is that the term shritzah (swarming) has an implication of movement. Thus he says of both sheretz and remes: richasha d’rachish (moving things that move)., which Onkelos translated, richasha d’rachish. Thus it is obvious that Onkelos understood both words (sheretz and remes) as conveying a sense of movement. He has explained it correctly. Shratzim are so called because of their constant movement. It is possible that it is a composite word: sheretz, shehu ratz (that which runs). Remes is so called because it creeps upon the earth and is never quiet or at rest.
Know that every winged creature that has four legs is called sheretz ha’oph (a winged creeping thing) because it leans on its legs and moves like shratzim, and a winged creature which is not so is called oph kanaph (winged fowl) because its main method of movement is flying. The meaning of the verse, ‘Veshartzu’ in the earth and be fruitful, and multiply upon the earth is thus: that they may walk upon the entire earth, and be fruitful and multiply upon it. ‘Shirtzu’ in the earth and multiply therein means “move about the entire earth and multiply thereon.” This is the reason for the repetition of the word ur’vu (and ye multiply) in the verse. [9:7]. Thus the first expression and multiply establishes the commandment of procreation; the second refers to the duty of making the whole earth habitable for people. This being so, we will explain the expression, which the waters ‘shartzu,’ as meaning “which the waters have moved and brought forth.” Similarly, the expression, ‘Vesharatz’ the river with frogs [means that the river moved and brought forth frogs]. Also, And the children of Israel were fruitful ‘vayishr’tzu,’, 1:7. means that they were fruitful and they multiplied and moved about because of their multitude until the land was filled with them.
Onkelos, however, interpreted the verse, ‘Shirtzu’ in the earth, as having reference to propagation. He thus translated, “Propagate in the land,” since he understood the word shirtzu — a verb — as being borrowed from the noun shratzim (reptiles). [The verse, according to Onkelos, thus states:] “And you, be ye fruitful and multiply, as the prolific creatures in the earth, and multiply therein.” Similarly, And the children of Israel were fruitful ‘vayishr’tzu’, 1:7. means they brought forth progeny abundantly as the prolific creatures.

יעופף על הארץ, even though its creation originated from the waters, it would grow to maturity on earth.

יעופף על הארץ על פני רקיע השמים, in order to cleanse the air of the atmosphere for the benefit of the inhabitants of the earth from any excessive moisture in the air which had resulted through the creation of the rakia on the second “day.”

ויאמר אלוקים ישרצו המים, the expression שריצה refers to multiple births, meaning multiple eggs being deposited for hatching. Seeing that the waters and the dry land had been completely separated by now, G’d decreed that each region was to produce offspring to perpetuate the various species of its habitat. The waters were addressed first, seeing they occupy the upper part of the globe. Not only that, but they had been first in the order of creation. G’d’s directive that a rakia be inserted had also preceded His directives to what should happen on earth. When addressing the waters directing that its inhabitants should multiply, G’d employed the plural mode ישרצו instead of the singular mode seeing there are so many different species of creatures which inhabit the oceans. When addressing the earth, ordering that the earth do something parallel, G’d used the singular mode תוציא, to let the reader know how relatively few species of creatures were involved in that directive.

שרץ נפש חיה, the reason why the word שרץ is in the singular mode has already been explained in connection with the expression תדשא הארץ דשא in verse 11. Another reason why the singular mode was chosen by the Torah here, may be that the word שרץ describes any moving creature, as implied by the Targum, רחשא, as in רחושי מרחשן שפוותיה, (Sanhedrin 67) meaning “they are moving their lips.” The words השורץ על הארץ in Genesis 7,21 also are a description of a certain type of motion on earth. Nonetheless, the word does not lose its original meaning, i.e. that it describes multiple reproduction by a certain species.

נפש חיה, an expression for anything equipped with the means to move of its own accord. What the earth had produced on the third “day” did not have the ability to move from the spot from which it emerged from the earth. It isנפש צומחת, a living plant, as distinct from נפש חיה, a mobile form of life.

ועוף יעופף על הארץ, the directive to multiply by means of multiple births applied also to the birds which are flying above the earth. The birds are composed primarily of a combination of factors found either in the air or in the sea.

על פני רקיע השמים, a reference to the atmosphere as we explained already. The Torah omitted to report specifically that this directive had been carried out as למיניהם, according to their respective species, not because the birds crossbreed, but in the interest of brevity. The word למיניהם at the end of verse 21 sufficed to make this point.