The Non-Inverting Amplifier and the Virtual Short
The feedback divider sets the gain
Sliding the feedback ratio Rf/Rg changes the length of the gold arrow on the output side. The input enters the lower + terminal, and the virtual short holds the upper V− equal to Vin. The Rf-Rg divider coming down from the output feeds part of Vout back to V−, and the op-amp raises its output until that fed-back voltage equals Vin, so the output becomes (1+Rf/Rg) times the input. Set the ratio so the gain is exactly 4, on the white dashed line.
Feed the input into the non-inverting input
Connect the input voltage Vin directly to the non-inverting input V+. As long as negative feedback is in place, the op-amp makes the two inputs equal in potential (the virtual short), so the inverting input V− also becomes Vin. In the inverting amplifier V+ was tied to ground and V− sat at 0V, but here V+ is Vin, so V− is pinned to Vin. No current flows between the two inputs, yet their potentials match: that is the virtual short, and the gold label on the upper input line in the plot marks it.
The feedback is a voltage divider
From the output Vout, Rf and Rg run in series down to ground, and the node between them touches V−. It is a voltage divider whose input is the output. No current enters the V− terminal, so the division is clean, and the voltage V− receives is Vout·Rg/(Rg+Rf). The virtual short makes this equal to Vin, so Vout·Rg/(Rg+Rf) = Vin, which rearranges to Vout = Vin·(Rg+Rf)/Rg = Vin·(1+Rf/Rg). The gain 1+Rf/Rg is the reciprocal of the fraction the divider feeds back, β = Rg/(Rg+Rf), so the smaller that fraction, the larger the gain.
Mirror of the inverting amplifier, and the follower
The inverting amplifier used a virtual ground (V−=0) to make a gain of −Rf/Rin; the non-inverting amplifier uses a virtual short (V−=Vin) to make a gain of 1+Rf/Rg. The inverting one flips the sign and can have a gain below 1, while the non-inverting one keeps the sign and always has a gain of 1 or more. Another advantage is that the input goes into the very large input resistance of V+, so it draws almost no current from the signal source. Set Rf to 0 or remove Rg and the gain becomes exactly 1: a voltage follower (buffer) that barely touches the input side while supplying plenty of current at the output.
Back to the first screen
As you slid the feedback ratio, the gold arrow grew to (1+Rf/Rg) times the input, and at Rf/Rg = 3 it reached exactly 4 times, on the white dashed line. One choice, feeding the input into the non-inverting input, pinned the inverting input to Vin, and while the divider coming down from the output fed part of it back, the op-amp pushed its output up until the two matched. The sign stays the same and the gain is always 1 or more. What the inverting amplifier did with a virtual ground, the non-inverting amplifier repeats, mirror-like, with a virtual short and a voltage divider.