"That is known as the Children's Hour."
At first the speaker says that the hour is between the dark and the daylight, suggesting that it is sometime right before the dawn. He then says the "night is beginning to lower" and there is a "pause in the day's occupations"; this means that it is actually in the evening as the sun is going down. The exact time of "Children's Hour" is thus a bit ambiguous, but what is important is that there is this cozy, intimate hour almost outside of time and space that is set aside for the hardworking father to receive the warm, playful embraces of his daughters. Time in this poem is boundary-less, fungible; it is love that is real and tangible.
"Till I think of the Bishop of Bingen / In his Mouse-Tower on the Rhine!"
This is an amusing allusion. This bishop was a tyrant who, according to a folktale, was devoured alive by mice in a tower outside a small German town. Although this a rather bleak story, it does ably convey the light, incessant, and fervent twittering and touches the daughters have for their father. It also adds to the fairytale nature of the poem.
"And there I will keep you forever, / Yes, forever and a day,"
This is a sweet but melancholy sentiment. It is of course impossible for the father to hold onto his daughters forever. They will grow old and move on to form their own families. Furthermore, he will grow old and will die, and sometime after that they too will die. The father is aware of the ephemerality of life, but rather than allowing the bleak reality to color his thoughts, he channels it into a loving proclamation. He suggests to his daughters that the love between them transcends life and death; it is comforting and sustaining in a way that only a father can provide.
"Do you think, O blue-eyed banditti, / Because you have scaled the wall, / Such an old mustache as I am / Is not a match for you all!"
Initially it is unclear how the father will react to the incoming attack from his daughters. The first several stanzas of the poem do not say anything about his state of mind (although the language he uses throughout the poem and the mood set from its inception indicate that he is receptive to what is coming; furthermore, the regularity implied by a "children's hour" suggests that it happens every night and so is likely palatable to him). We only hear the girls' plotting and then finally see their ambush. Right away, though, it becomes clear that he is happy they are swarming around him and devouring him with kisses. By calling them "banditti" he keeps up the playful spirit and lets them know their presence and embraces are welcome.