What does "to-" in today, tomorrow, tonight mean?

Solution 1:

It is a prefix that in some cases ( like today ) has survived from Middle English usage in words with reference to time meaning on ( this day):

Today:

• Old English todæge, to dæge "on (this) day," from to "at, on" (see to) + dæge, dative of dæg "day" (see day). Meaning "in modern times" is from c. 1300. As a noun from 1530s. Generally written as two words until 16c., after which it usually was written to-day until early 20c.

To:

• Old English to "in the direction of, for the purpose of, furthermore," from West Germanic *to (cognates: Old Saxon and Old Frisian to, Dutch too, Old High German zuo, German zu "to"), from PIE pronominal base *do- "to, toward, upward" (cognates: Latin donec "as long as," Old Church Slavonic do "as far as, to," Greek suffix -de "to, toward," Old Irish do, Lithuanian da-), from demonstrative *de-.

• Commonly used as a prefix in Middle English (to-hear "listen to," etc.), but few of these survive (to-do, together, and time references such as today, tonight, tomorrow -- Chaucer also has to-yeere). To and fro "side to side" is attested from mid-14c. Phrase what's it to you "how does that concern you?" (1819) is a modern form of an old question:

(Etymonline)

Solution 2:

The "to" is the versatile preposition, which comes to us from Old English. It has a temporal meaning of on (a day) or in (a time). Others? Sure. "Together" and "toward." The "to" has a different meaning in locational use.