Newman projection is a short hand way to represent a molecule looking straight down a bond connecting two carbons. Let’s take a look at a molecule below.

In the picture below, imagine looking standing to the left and looking at the first carbon. You will see group A on top, group B to the left and group C to the right. Behind the first carbon is the second carbon, represented by the blue circle in the Newman projection. You will see group F at the bottom, group D to the left and group E to the right. This conformation is called staggered because the groups on the first carbon are spread out from the groups in the second carbon.
The picture at the bottom is that of eclipsed conformation where the groups of the front and back carbons are right behind each other.

Staggered and eclipsed Newman projections

Note: Staggered conformation is always more stable and lower energy that eclipsed conformation. This is due to a number of different factors.
First, in a staggered conformation there is a stabilizing interaction between C-H sigma bonding molecular orbital of one carbon and a C-H sigma antibonding molecular orbital on a different carbon. The electrons in the filled bonding molecular orbital can partially move into unoccupied anti bonding molecular orbital. This delocalization of electrons is called hyper conjugation and is only possible in the staggered conformation (the two orbitals are parallel to each other and can overlap).
Also, in a staggered conformation, the groups are further away from one another avoiding steric hindrance.

Conformations Of Butane

Let’s draw all of the conformations of butane looking at the C2-C3 bond as the arrow is pointing. Carbon number 2 is attached to two hydrogens and one methyl group. Carbon number 3 is also attached to two hydrogens and one methyl group. I am starting with an eclipsed conformation, but you can start with any conformation you would like to draw. To get to the next conformation, I keep the front carbon and its groups the same and I rotate the back carbon, getting to a staggered conformation. It should go eclipsed, staggered, eclipsed, staggered and so on.

Conformations Of Butane
Conformations Of Butane

Let’s now determine which conformation is most stable and which is least stable.
Staggered conformations are more stable than eclipsed. Conformations B, D and E should be lower in energy and more stable than conformations A, C, and E. Out of all the staggered conformations, D should be lowest in energy because it has two big groups (methyls) opposite one another. This conformation is called ANTI. The other two staggered conformations have two methyl groups next to one another, which is unstable. These are called GAUCHE.
The conformation that is least stable and highest in energy will be A because not only is it eclipsed, but it has methyls right behind one another.

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References:
Organic Chemistry by Paula Yurkanis Bruice
Organic Chemistry by David Klein

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