I have presented my own research on Karl Friston's Free Energy Principal so I will outline what each term means and then explain how they work within the three equations for you.
The symbols in the three equations have the following meanings.
$\tilde{s}$ denotes the observed data.
$\Psi$ denotes hidden (latent) variables of the model.
$m$ denotes the generative model.
$\mu$ denotes parameters of the variational distribution.
$p(\tilde{s},\Psi|m)$ is the joint probability of the data and latent variables under the model.
$p(\Psi|\tilde{s},m)$ is the true Bayesian posterior distribution.
$p(\Psi|m)$ is the prior distribution over the latent variables.
$p(\tilde{s}|\Psi,m)$ is the likelihood of the data given the latent variables.
$q(\Psi|\mu)$ is the variational approximation to the posterior.
$\langle f(\Psi)\rangle_q$ denotes the expectation of a function with respect to $q(\Psi|\mu)$:
$$
\langle f(\Psi)\rangle_q
=
\int q(\Psi|\mu)f(\Psi)d\Psi
$$
$D(q||p)$ denotes the Kullback–Leibler divergence
$$
D(q||p)
=
\int q(\Psi|\mu)\ln\frac{q(\Psi|\mu)}{p(\Psi)}d\Psi
$$
$p(\tilde{s}|m)$ is the model evidence (marginal likelihood)
$$
p(\tilde{s}|m)=\int p(\tilde{s},\Psi|m)d\Psi
$$
$F$ denotes the variational free energy.
The first equation
$$
F=-\langle\ln p(\tilde{s},\Psi|m)\rangle_q+\langle\ln q(\Psi|\mu)\rangle_q
$$
defines free energy as the expected negative log joint probability plus the expected log of the variational density.
The second equation
$$
F=D(q(\Psi|\mu)\ ||\ p(\Psi|\tilde{s},m))-\ln p(\tilde{s}|m)
$$
shows that free energy equals the KL divergence between the variational posterior $q(\Psi|\mu)$ and the true posterior $p(\Psi|\tilde{s},m)$ minus the log model evidence.
Since the KL divergence is non-negative, minimizing $F$ minimizes the divergence between the approximate and true posterior.
The third equation
$$
F=D(q(\Psi|\mu)\ ||\ p(\Psi|m))-\langle\ln p(\tilde{s}|\Psi,m)\rangle_q
$$
decomposes free energy into a complexity term and an accuracy term.
The first term
$$
D(q(\Psi|\mu)\ ||\ p(\Psi|m))
$$
measures the divergence between the variational posterior and the prior.
The second term
$$
\langle\ln p(\tilde{s}|\Psi,m)\rangle_q
$$
is the expected log likelihood of the observations under the variational distribution.
Thus free energy can be interpreted as
$$
F = \text{complexity} - \text{accuracy}.
$$
All three expressions represent the same quantity but highlight different interpretations of variational free energy.
