In Variational Quantum Eigensolvers, what does "grouping Pauli operators into tensor products requiring the same post-rotations" mean?

Let me show an example for grouping for this Hamiltonian:

$$H = 5 cdot XI + 3 cdot XZ - 2 cdot YI + 1.5 cdot IY$$

The expectation value:

$$langle H rangle = 5 cdot langle XI rangle + 3 cdot langle XZ rangle - 2 cdot langle YI rangle + 1.5 cdot langle IY rangle$$

Here I will group them in this way: the first group $XI$ and $XZ$, the second group $YI$ and $IY$. Note that (it is important) the members of the same group should commute with each other. Also, I should mention that this is not the only way of grouping.

For the first circuit:

begin{align} &langle X I rangle = p(text{00 or 01 measurements}) - p(text{10 or 11 measurement}) &langle X Z rangle = p(text{00 or 11 measurements}) - p(text{10 or 01 measurement}) end{align}

For the second circuit:

begin{align} &langle Y I rangle = p(text{00 or 01 measurements}) - p(text{10 or 11 measurement}) &langle I Y rangle = p(text{00 or 10 measurements}) - p(text{01 or 11 measurement}) end{align}

where $p$ denotes a probability of a measurement outcome described in parenthesis. The main idea here is: For a given Pauli term $P$ the expectation value is equal to:

$$langle P rangle = p_+ - p_-$$

where $p_+$ ($p_-$) is the probability of having an eigenstate that has eigenvalue $+1$ ($-1$). More details about this can be found in this answer about expectation value estimation. About why $HS^{dagger}$ is applied in the second circuit can be understood from this answer.