The logbook is an item found inside a physical geocache to be signed by everyone who finds the cache.
A logbook is one of the traditional items found inside a geocache. The size of the logbook will vary depending on the cache size. Some of the smallest caches may only contain a folded up strip of paper. Some of the larger caches may contain a small notebook.
When a cache is found, it is customary to sign it with the finder's Geocaching.com handle and the date. It used to be quite common to write out a log, much like might be done online. With the increase in smaller caches, it has become more common to just use the name and date.