today: on this present day, the day now happening
This is the ordinary Greek word for today. It points to the day the speaker is standing in, whether that is the day bread is needed (give us today our daily bread), the day a healing is witnessed, or the day a trial is held. In the fixed phrase to this day it stretches slightly, marking that some situation has lasted right up to the present moment.
The word carries no hidden meaning of its own, yet the New Testament often sets it in weighty sentences, and there the plain today becomes charged. Luke uses it for the arrival of salvation in the present: today a Savior is born, today this Scripture is fulfilled in your hearing, today salvation has come to this house, today you will be with me in paradise. In each case the force comes from what God is doing on this particular day, not from a special sense buried in the word.
Hebrews presses the word hardest. Quoting a psalm that begins Today, if you hear his voice, it treats that today as the still-open window of God's invitation: as long as it is called Today, do not harden your hearts. The same book, with Acts, applies the psalm line today I have begotten you to the Son, and rounds off with the confession that Jesus Christ is the same yesterday and today and forever. The urgency readers feel in these lines belongs to the moment God has appointed, and the small word today simply names it.