means The work of cutting down trees and hauling away the timber, typically as an industry — and, in computing, the act of recording events or data over time.

from Rooted in "log," the Old Norse-derived word "lág" for a felled tree or trunk, which English took up by the 14th century. The trade of cutting timber gave us "logging." The computing sense rides on a sailor's pun: ships once measured speed by tossing a "log" (a wooden float) overboard and timing it, recording the result in the "logbook" — so "to log" came to mean keeping a running record, and that meaning sailed into the digital world.