When. Throughout the day, in the gaps: walking, waiting, between tasks. Four words, requiring no particular state and no set time.
The words. Two verbs, and the second is the one usually skipped over. Astaghfirullah — I seek forgiveness of Allah — is the request. Wa atubu ilayh — and I turn to Him — is a different act. Tawbah is from the root t-w-b, to return; the verb describes a movement back toward something, not an apology. Asking to be forgiven and actually turning around are two things, and the formula does not let a person say the first without the second.
The preposition ilayh, "to Him", makes the direction explicit. Repentance in the language is not merely leaving something behind — it is going somewhere.
Whose practice this is. This is the striking part. The one who repeated it was the one with the least to repent for, and he is transmitted as saying it many times a day. Whatever a person concludes from that, the conclusion cannot be that istighfar is proportional to sin.
On the counts. The two best-known reports give different numbers. In al-Bukhari (6307) he says he seeks Allah's forgiveness and repents to Him more than seventy times a day; in Muslim (2702) he says he repents to Allah a hundred times a day. The variation is in the accounts themselves. Repeating it a hundred times is a widespread practice, and the number is a habit-forming device, not a threshold that unlocks anything.
Common confusion. This short formula is not Sayyidul Istighfar, which is far longer and belongs to the morning and evening remembrance. This one has no fixed time at all, which is exactly why it accumulates.