Nautical time keeping (8 bells pattern)

Unlike civilian clock bells, the strikes of the bell do not match the number shown on the dial of the clock. Instead, there are eight bells, one for each half-hour of a four-hour watch. When ships were run by sail power alone,  watches were timed with a thirty-minute hourglass. Bells would be struck every time the glass was turned, and in a pattern of pairs for easier counting, with any odd bells at the end of the sequence.
The classical system was:

Number of bells	Bell Pattern	Middle watch	Morning watch	Forenoon watch	Afternoon watch	First dog watch	Last dog watch	First watch
One bell	.	0:30	4:30	8:30	12:30	16:30	18:30	20:30
Two bells	..	1:00	5:00	9:00	13:00	17:00	19:00	21:00
Three bells	.. .	1:30	5:30	9:30	13:30	17:30	19:30	21:30
Four bells	.. ..	2:00	6:00	10:00	14:00	18:00		22:00
Five bells	.. .. .	2:30	6:30	10:30	14:30		18:30	22:30
Six bells	.. .. ..	3:00	7:00	11:00	15:00		19:00	23:00
Seven bells	.. .. .. .	3:30	7:30	11:30	15:30		19:30	23:30
Eight bells	.. .. .. ..	4:00	8:00	12:00	16:00		20:00	0:00

At midnight on New Year's Eve sixteen bells would be struck – eight bells for the old year and eight bells for the new.
Most of the crew of a ship would be divided up into between two and four groups called watches. Each watch would take its turn with the essential activities of manning the helm, navigating, trimming sails, and keeping a lookout.
The hours between 16:00 and 20:00 are so arranged because that watch (the "dog watch") was divided into two. The odd number of watches aimed to give each man a different watch each day. It also allows the entire crew of a vessel to eat an evening meal, the normal time being at 1700 with First Dog watchmen eating at 1800.
Some "ship's bell" clocks use a simpler system:

Number of bells	Bell Pattern	Hour (a.m. and p.m.)
One bell	.	12:30	4:30	8:30
Two bells	..	1:00	5:00	9:00
Three bells	.. .	1:30	5:30	9:30
Four bells	.. ..	2:00	6:00	10:00
Five bells	.. .. .	2:30	6:30	10:30
Six bells	.. .. ..	3:00	7:00	11:00
Seven bells	.. .. .. .	3:30	7:30	11:30
Eight bells	.. .. .. ..	4:00	8:00	12:00

The term "Eight bells" can also be a way of saying that a sailor's watch is over, for instance, in his or her obituary. It is a nautical euphemism for "finished".
Ship's bells are also used for safety in foggy conditions, their most important modern use.  On naval vessels, bells additionally are rung as "boat gongs" for officers and dignitaries coming aboard or leaving the ship, in a number equivalent to the number of side boys to which the visitor is entitled.  (a side boy is a member of an even-numbered group of seamen posted in two rows at the quarterdeck when a visiting dignitary boards or leaves the ship, historically to help him aboard)
The ship's name is traditionally engraved or cast onto the surface the bell, often with the year the ship was launched as well. Occasionally (especially on more modern ships) the bell will also carry the name of the shipyard that built the ship.  If a ship's name is changed, maritime tradition is that the original bell carrying the original name will remain with the vessel. A ship's bell is a prized possession when a ship is broken up, and often provides the only positive means of identification in the case of a shipwreck.
Most United States Navy ships of the post-World War II era have actually carried two ship's bells: the official bell on deck, and a smaller one in the pilot house at the 1MC (public address) station, used when the ship is underway.