ט־ו־ב is one of the very first words a learner meets, טוֹב, "good". It is a hollow root: the middle letter is a vowel (ו), so the consonants you really hear are ט and ב around an oo/o sound. From this single idea Hebrew builds the adjective (good), the abstract quality (goodness, bounty), a concrete kindness (a favour), and even an adverb for doing something well. The thread is plain: one root, the whole bandwidth of "good", from a moral state to a small act of kindness. Every word here is verified against pealim, niqqud included.
The same root runs through the verb system. Each binyan is a voice: it bends the one idea into active, passive, causative or reciprocal. Tap to hear.
The verb לָטוּב is biblical and barely used in modern speech, which is why ט־ו־ב lives almost entirely as an adjective and a set of nouns. Being a hollow root (middle ו), it never spreads across the seven binyanim the way a strong root does; the everyday "to improve / make better" idea is carried by the related root י־ט־ב (e.g. הֵיטֵב below).
Same root letters, different noun moulds (mishkalim). The mould tells you the function: who does it, the act of doing it, or the thing produced.
Strip the prefixes, suffixes and vowels. Three consonants remain, and the meaning lives there.