The speaker seems to work at a school, and the end of the year has brought a flood of farewells: students heading to high school or other schools, teachers moving on, and the head of school leaving too. After weeks of searching for warm, creative ways to say goodbye to each person, the speaker is tired and wants a way to be finished. The answer is an imagined box that holds every tear, hug, wave, cheer and "I'll miss you," then gets taped shut until next year.
The second part compares goodbyes to a game of Bingo. You mark your card, the squares fill up, someone shouts "BINGO," and it's over, whether you won or lost. The repeated "it's over" sounds tired and a little numb. The mood is bittersweet and weary. The speaker cares deeply, but the "fluttery feelings of heartache" are ones they "don't want to feel anymore," so the poem reads as a quiet attempt to protect themselves until endings come around again.