The moon is spherical.
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The Moon is there, but the side that's reflecting the Sun's light is facing away from Earth. As the Moon moves around Earth in its orbit, the light reflecting off the side of the Moon creates a sliver of shape. This is a crescent moon.
The general term for the visible lit part of the moon is "the phase of the moon." The visible lit portion can have a crescent shape, a gibbous shape or a "half-moon" (half circle) shape.
The first crescent moon occurs when the moon appears as a thin, curved shape in the sky shortly after the new moon phase. It is often the first visible phase of the moon in the lunar cycle and marks the beginning of the waxing phase.
The Moon's shape on Monday would have been a waxing gibbous, which appears as a rounded shape with a larger illuminated portion compared to a first quarter Moon.
crescent moon