Pulp is a soft, squishy, or slightly wet mush. The soft inside part of your tooth is pulp, and the soft flesh of a peach is also pulp.
There are many kinds of pulp, including the soggy stuff that starts out as trees and ends up as paper. The process of turning wood into paper starts with pulp, the stripped wood fibers that are steamed and ground or mixed with chemicals before being bleached and dried. Magazines printed on very rough, inexpensive paper were once also referred to as pulps, leading to the name "pulp fiction" for cheap, sensational books and magazines.