The table lists the coming primary phases of the moon, in order, from the U.S. Naval Observatory: new moon, first quarter, full moon and last quarter. The key facts at the top give the next full moon in a sentence.
Reading the times
The Naval Observatory gives the date and time of each phase in Universal Time. This page also shows each time in Eastern time. Because of the conversion, a phase early in the day in Universal Time can fall on the previous evening in the United States, and the Eastern column shows that date.
When it updates
The Naval Observatory computes these times in advance. This page reads them every few hours and updates at the same address, so the table always starts from the next phase.