This particular week has been chosen because the Moon will remain high above the horizon during the early evening, and following sunset. When the Moon is high in the sky we tend to get a much clearer view, so should be able to see craters, mountains and even the Lunar Mare or seas. During the week long event, observers will see the phase of the Moon change from a crescent shape, through first-quarter on the 2nd April (i.e. half-illuminated) and onto gibbous phase by the end of the week.
If you would like to particpate in this project, you can get more information on the official Spring Moonwatch website.