  We report the properties of more than 800 bursts detected from the repeating
fast radio burst (FRB) source FRB 20201124A with the Five-hundred-meter
Aperture Spherical radio Telescope (FAST) during an extremely active episode on
UTC September 25-28, 2021 in a series of four papers. In this second paper of
the series, we mainly focus on the energy distribution of the detected bursts.
The event rate initially increased exponentially but the source activity
stopped within 24 hours after the 4th day. The detection of 542 bursts in one
hour during the fourth day marked the highest event rate detected from one
single FRB source so far. The bursts have complex structures in the
time-frequency space. We find a double-peak distribution of the waiting time,
which can be modeled with two log-normal functions peaking at 51.22 ms and
10.05 s, respectively. Compared with the emission from a previous active
episode of the source detected with FAST, the second distribution peak time is
smaller, suggesting that this peak is defined by the activity level of the
source. We calculate the isotropic energy of the bursts using both a partial
bandwidth and a full bandwidth and find that the energy distribution is not
significantly changed. We find that an exponentially connected broken-power-law
function can fit the cumulative burst energy distribution well, with the lower
and higher-energy indices being $-1.22\pm0.01$ and $-4.27\pm0.23$,
respectively. Assuming a radio radiative efficiency of $\eta_r = 10^{-4}$, the
total isotropic energy of the bursts released during the four days when the
source was active is already $3.9\times10^{46}$ erg, exceeding $\sim 23\%$ of
the available magnetar dipolar magnetic energy. This challenges the magnetar
models invoking an inefficient radio emission (e.g. synchrotron maser models).
