|ג וַיַּעֲשׂוּ-כֵן הַחַרְטֻמִּים, בְּלָטֵיהֶם; וַיַּעֲלוּ אֶת-הַצְפַרְדְּעִים, עַל-אֶרֶץ מִצְרָיִם.||3 And the magicians did in like manner with their secret arts, and brought up frogs upon the land of Egypt.|
I am not considering the issue of how Moshe managed to bring up frogs, or whatever tzefarde'im are. That was a nes, which either means Hashem's close control over nature to direct all those frogs, or else something outside the realm of nature, depending on how you take your miracles. But what about the chartumim?
Well, one could say that magic is real, and they practiced it. The rationalists amongst us won't like this much, though.
Shadal has an interesting suggestion, in which the secret art they knew was science, and, well ...
ויעשו כן החרטומים בלטיהם : לקחו כלי מלא מים שהיו בהם ביצי צפרדע, ובלטיהם (בחכמת הטבע) מיהרו יציאת הצפרדעים מן הביצים
"They took vessels full of water which had in them frog eggs, and with their lateihem (with scientific knowledge) they sped up the exiting of the frogs from the eggs."
Is such a thing possible? Indeed, it seems to be.
To cite a Wikipedia article on Frogs:
The eggs of some species laid out of water can detect vibrations of nearby predatory wasps or snakes, and will hatch early to avoid being eaten.The Wikipedia article was citing Warkentin, K.M. (1995). "Adaptive plasticity in hatching age: a response to predation risk trade-offs". Proceedings of the National Academy of Sciences 92: 3507-3510.
That article is available here.
A separate question was whether this scientific knowledge, or something akin to it, was available in the time of Shadal. And a separate question is whether such knowledge was available in ancient Egyptian times. And a separate question is whether this is a plausible explanation of the pasuk, given context. All these questions, I'm not addressing here.