This is known as a Waxing Crescent Moon.  This Moon can be seen after the New Moon, but before the First Quarter Moon.  The crescent will grow larger and larger every day, until the Moon looks like the First Quarter Moon.

This Moon is known as a Waxing Gibbous Moon.  This Moon can be seen after the First Quarter Moon, but before the Full Moon.  The amount of the Moon that we can see will grow larger and larger every day.  ("Waxing" means increasing, or growing larger.)

This Moon is called a Waning Gibbous Moon.  This Moon can be seen after the Full Moon, but before the Last Quarter Moon.  The amount of the Moon that we can see will grow smaller and smaller every day. ("Waning" means decreasing, or growing smaller.)

This Moon is called the Waning Crescent Moon.  This Moon can be seen after the Last Quarter Moon and before the New Moon.  The crescent will grow smaller and smaller every day, until the Moon looks like the New Moon.