A solo project usually refers to a single member of a band

Musical ensemble

A musical ensemble is a group of people who perform instrumental or vocal music. In classical music, trios or quartets either blend the sounds of musical instrument families or group together instruments from the same instrument family, such as string ensembles or wind ensembles...

's work independent of their original group, yet typically without having quit their original group. It can also refer to a musical project originally containing only one member rather than an ensemble.
Some very well known solo projects are Phil Collins

Phil Collins

Philip David Charles "Phil" Collins, LVO is an English singer-songwriter, drummer, pianist and actor best known as a drummer and vocalist for British progressive rock group Genesis and as a solo artist....

, Owl City

Owl City

Owl City is an American electronica musical project by singer-songwriter and multi-instrumentalist Adam Young formed in 2007 in Owatonna, Minnesota. Young created the project while experimenting with music in his parents' basement...

, Never Shout Never, Secondhand Serenade

Secondhand Serenade

Secondhand Serenade is an American acoustic rock band, led by vocalist and guitarist John Vesely. Vesely has released three studio albums to date under the name Secondhand Serenade: Awake in 2007, A Twist in My Story in 2008 and Hear Me Now in 2010...

, and most notably Nine Inch Nails

Nine Inch Nails

Nine Inch Nails is an American industrial rock project, founded in 1988 by Trent Reznor in Cleveland, Ohio. As its main producer, singer, songwriter, and instrumentalist, Reznor is the only official member of Nine Inch Nails and remains solely responsible for its direction...

.