What is the meaning of "Yabi'a"?
Rashi citing Menachem: It is an expression of a spring that is Nove'a (flows).
Radak: Yabi'a is speaking, like "Yabi'un b'Fihem", "Tabanah Safasai" (Tehilim 59:8, 119:171).
Why does it say "Yom l'Yom Yabi'a Omer"?
Rashi: The act of creation is renewed every day. At night the sun sets, and it shines in the morning. Amidst this, people praise via the days and nights, which instruct people to praise and thank.
Radak: Today speaks about the coming day (that it will be so), and the night about the coming night. I.e. the order of the motions of day and night, like from the six days of Creation, so it is and will be forever. Nothing changed.
Malbim #1: There are three ways to clarify that something was done with intent, and not by chance. (a) Frequency - chance occurs only infrequently. (b) Chachmah - if it was made with perfection. Chance occurrences are not perfect. (c) Purpose. Chance occurrences are not for a purpose. If it is for a purpose, it is not chance, like the philosopher said (Sefer ha'Shma, 2). We know Kevod Kel from the creation in general - (a) Via the multitude. Every day man sees acts of Hashem and tells His Gevurah. (b) The sphere is always turning. Every day 'tells' the next day to come, and similarly regarding nights. The increase is constant.
What is "Yechaveh"?
Rashi: It is Hagadah (telling).
Why does it say "v'Laylah l'Laylah Yechaveh Da'as"?
Malbim: At night nature is quiet. It is time of thought, to investigate what one saw and heard during the day, and derive Da'as of Elokim. Every day there are new Chidushim of Elokim; so at night there are new revelations of His acts.