For a lunar eclipse to occur, a full moon must also be occurring. When full moons occur, the earth is opposite from the Sun, which allows the planets are lit up. If the Earth, Sun, and Moon are all aligned, the moon will turn to dark. If it is dark, an eclipse is not able to occur.
For an eclipse, a full moon is a necessary part. While they are necessary, a lunar eclipse is not guaranteed to show during every full moon. This is because the moon must be near a node of the junction, which should be between the planes of the orbit and the ecliptic.
The earth needs to be directly opposite from the sun for a lunar eclipse to occur. This occurrence is during a full moon when the side of the planet is lit up and observed by inhabitants of the earth. When the earth, sun, and moon are perfectly aligned, or as close to perfect as they may achieve, the moon creates an umbra and a penumbra, and this creation means that the moon turns to dark.
The appearance of a full moon during an eclipse is necessary. Lunar eclipses will appear at the time of the full moon, but not every full moon because the moon needs to be near one of the nodes of the junction between its orbit and ecliptic plane.