Approximately 1 petabyte.
The capacity of human memory can only be estimated within very rough limits, as our understanding of its structure is still limited. The estimate presented in 2015 at the Salk Institute for Biological Studies (California, USA) is based on the assumption that the process of memorization is related to the formation of synaptic connections between neurons.
A careful count of synapses in a small area of brain tissue showed that their number can reach 2–3 quadrillion (2.5×1015) — about 25 thousand per neuron. Synapses have two to three dozen different states, allowing them to store 4–5 bits of information. Thus, the total capacity of the brain is about 1015 bits, which is equivalent to 1 petabyte. This roughly corresponds to a thousand high-capacity hard drives.
This memory primarily supports the functioning of the organism. What we can consciously recall constitutes only a tiny fraction of this volume. It is unlikely that the brain's storage can be overwhelmed with excessive memories, as the very process of memorization — the formation of synaptic connections — occurs quite slowly.