Children always want to ask question after question; parents shouldn't get annoyed.
Tips
memory
The pun is on 璺 (wèn, a crack in pottery) and 问 (wèn, to ask) — both pronounced wèn. When a sand pot (砂锅) cracks, the crack runs all the way to the bottom (问到底 = 璺到底). The image: keep cracking/questioning until the fracture reaches the very bottom.
history
Recorded in modern educator Tao Xingzhi's 《普及现代生活教育之路》. The variant 打破沙锅问到底 (沙 instead of 砂) is equally common and has the same meaning.