There are five common uses for Y-cables in signal paths: A Y-cable common in domestic settings has a stereo 3.5mm (1/8″) stereo male minijack at one end, to plug into the line- or headphone-output of an MP3 player, mobile phone, or computer soundcard, and a pair of RCA (phono) male plugs to connect to the left and right mono inputs of an external amplifier.
In older desktop PCs, PATA (aka "IDE") devices such as 5.25 inch optical drives and 3.5 inch hard drives are typically powered by means of Molex connector Y-cables.
As long as the host has two available USB sockets, this enables a peripheral that requires more power than one USB port can supply (but not more than two ports can supply) to be used without requiring a mains adaptor.
A newer variant on this kind of cable allows a USB peripheral to receive data and power from two different devices respectively.
This allows power-hungry peripherals to be used with sockets that are designed to supply little or no outgoing power, such as USB On-The-Go mini-B sockets on smartphones.