How does the word "today" make sense?

Solution 1:

"To-day" comes from Old English and means "on the day" similarly to how "to-morrow" means "on the morning". You will also see "On the morrow" in older writing.

today [alternative forms: to-day (archaic)]

Etymology

Via Middle English today, from Old English tōdæġ, tō dæġe (“on [the] day”), made from tō (“at, on”) + dæġe, the dative of dæġ (“day”).

[Wiktionary]