How are memories saved?

Sci-American gives a brief answer:

"Understanding exactly how the brain encodes and stores memories is one of the central, unsolved mysteries in neuroscience. Currently the most widely accepted theory is long-term potentiation (LTP)—the lasting communication established between two neurons when they are stimulated simultaneously.

As a person processes an event, two neurons pass information through a small space called a synapse. This chemical conversation triggers an intricate cascade, inviting nearby neurons to fire and ultimately creating a network of connections with varying strengths. Afterward, this pattern of connections, or memory, remains within the network of neurons that processed the event.

Although many areas of the brain contain synapses capable of creating strong patterns of connectivity, the hippocampus is a particularly favorable spot for recording memories. This brain region plays a critical role in learning new information, forming spatial memories and storing short-term memories as long-term ones.

Memories formed with the hippo­campus are especially rich because they integrate input from several areas of the brain, and the ­hippocampus contains densely packed layers of neurons. In addition, damage to this region and nearby areas causes profound and perm­anent amnesia—an inability to store new memories or to recall old ones—and is observed in patients who have Alz­heimer’s disease."