A titanium ball valve is a titanium valve with a spherical disc (or ball) that works to control the flow through it. The ball (sphere) has a hole (known as a port) that when “in line” or “open” allows flow to occur. When the valve is closed the hole is perpendicular to the ends of the valve thus stopping flow. 
titanium ball valves are typically operated with a lever, gear, or an actuator. They are part of the quarter turn family meaning that the opening mechanism needs to be turned a quarter (or 90 degrees) to open or close the valve. 
They are en excellent choice for shutoff applications; however typically do not offer fine control necessary for throttling applications. 
There are five general body styles of titanium ball valves: single body, three piece body, split body, top entry, and welded. The difference is based on how the pieces of the valve—especially the casing that contains the ball itself—are manufactured and assembled. The valve operation is the same in each case. 
In addition there are different styles related to the bore of the ball mechanism:

A full port, or more commonly known full bore titanium ball valve, has an over-sized ball so that the hole in the ball is the same size as the pipeline resulting in lower friction loss. Flow is unrestricted but the valve is larger and more expensive so this is only used where free flow is required, for example in pipelines which require pigging (a method use to clean pipes).

In reduced port, or more commonly known reduced bore titanium ball valves, flow through the valve is one pipe size smaller than the valve’s pipe size resulting in the flow area being smaller than the pipe. As the flow discharge remains constant and is equal to area of flow (A) times velocity (V), A1V1 = A2V2 the velocity increases with reduced area of flow.

A V port titanium ball valve has either a ‘v’ shaped ball or a ‘v’ shaped seat. This allows the orifice to be opened and closed in a more controlled manner with a closer to linear flow characteristic. When the valve is in the closed position, and opening is commenced, the small end of the ‘v’ is opened first, allowing stable flow control during this stage. This type of design requires a generally more robust construction due to higher velocities of the fluids, which might damage a standard valve.

A trunnion titanium ball valve has an additional mechanical anchoring of the ball at the top and the bottom, suitable for larger and higher pressure valves (say, above 10 cm and 40 bars).

Cavity filler titanium ball valve. Many industries encounter problem with residues in the titanium ball valve. Where the fluid is meant for human consumption, residues may also be a health hazard, and as the fluid changes from time to time, contamination of one fluid with another may occur. Residues arise because in the half open position of the titanium ball valve a gap is created between the ball bore and the body in which fluid can be trapped. To avoid the fluid getting into this cavity, the cavity has to be plugged, which can be done by extending the seats in such a manner that it is always in contact with the ball. This type of titanium ball valve is known as Cavity Filler titanium ball valve.

titanium ball valves can also be made in a three-way or four-way design. These designs are usually L or T shaped with a hole in the middle. Such valves are used to divert flow to multiple ports at the same time.