The earth rotates one complete turn every 24 hours – giving us day. The moon orbits the earth, but I don’t think it’s synchronised with the earth’s rotation. If you look at a calendar of moonrises and moonsets, you can see that it rises and sets at prettymuch any time of the day or night: https://www.timeanddate.com/moon/uk/cambridge – I guess we associate the moon with nighttime because when it’s up in the day, the sun is out – and the sun is far more noticeable than the moon!
I hadn’t actually realised that the moon does its own thing, rising and setting on a schedule independent from day and nighttime. That’s weird. Essentially, it seems like you can see the moon in the day if it happens to be above the horizon at that point, in a biggish phase (ie probably not looking crescent-shaped), and not too close in the sky to the sun (whose brightness would drown it out). Apparently it’s out in the daytime about as often as at night!
To me, the question should be ‘why can’t we see the moon during the day’? As Yo explained below, the moon can rise and set at any time of our earthly day but we tend to only notice it during the night. That’s because the sun is so bright in the daytime that it ‘outshines’ the moon.