tovel

The verb טָבַל taval appears 16 times in the Tanakh. In almost all of them, it means "to dip, to immerse" (something in a liquid). In one verse, however, it means to immerse oneself:

וַיֵּרֶד וַיִּטְבֹּל בַּיַּרְדֵּן שֶׁבַע פְּעָמִים כִּדְבַר אִישׁ הָאֱלֹהִים וַיָּשׇׁב בְּשָׂרוֹ כִּבְשַׂר נַעַר קָטֹן וַיִּטְהָר׃

"So he [Naaman] went down and immersed himself in the Jordan seven times, as the man of God had bidden; and his flesh became like a little boy’s, and he was pure." (Melachim II 5:14)

The use of the kal form taval to describe ritual dipping in water is familiar from Talmudic and later Hebrew (along with the gerund tevila טְבִילָה - "immersion.") But in rest of Tanakh, the verb rachatz רחץ is used for such bathing. In fact, in the same story of Naaman, we find use of rachatz in the previous verse: רְחַץ וּטְהָר - "bathe and be pure."

Since in Rabbinic Hebrew taval generally referred to ritual immersion of a person in a mikveh, the other forms of the verb (absent in biblical Hebrew) were added for the dipping of things like food in liquids. Perhaps most famous of them is the dipping done at the Pesach seder. One of the four questions refers to it, and it also appears in the Mishna (Pesachim 10:4). The two most common versions of the question read today ask:

 שֶׁבְּכָל הַלֵּילוֹת אָנוּ מַטְבִּילִין פַּעַם אַחַת, הַלַּיְלָה הַזֶּה שְׁתֵּי פְעָמִים

"On all other nights we dip [our food] once; [however] on this night we dip twice."

Or alternatively:

שֶׁבְּכָל הַלֵּילוֹת אֵין אָנוּ מַטְבִּילִין אֲפִילוּ פַּעַם אֶחָת – הַלַּיְלָה הַזֶּה שְׁתֵּי פְעָמִים.

"On all other nights we do not dip [our food] at all; [however] on this night we dip twice."

I won't get into the question about which account of normal dipping is accurate (see Safrai's commentary for a discussion). But I do want to point out that the verb for dipping here is מַטְבִּילִין matbilin - in the hifil form. However, in many manuscripts of the Haggadah and Mishna we find the verb in the piel form: מְטַבְּלִים mitablim. Both piel and hifil here are transitive verbs - describing dipping something else. I haven't seen evidence that there was a distinction between them in Talmudic usage. Yet, they are clearly distinct from the common meaning of tovel: ritual immersion of a person in the mikveh.

These distinctions continued throughout Medieval Hebrew, but in Modern Hebrew, there is a return to the biblical usage. While taval in a religious sense can still refer to ritual immersion, it is also used for dipping of food in liquids or sauces. The hifil verb, הִטְבִּיל hitbil, is generally reserved for the transitive act of ritually immersing someone else in water - i.e., baptism. 

And what about the piel form טִבֵּל tibel? While it does mean "to dip," it seems that it fell out of favor due to the similar sounding תִּבֵּל tibel - "to spice, flavor, season." While Hebrew can handle homonyms, in this case both words not only refer to food, but specifically to adding something else to food, which would be confusing. So by returning to the biblical taval, the distinction between dipping and seasoning remained clear.