The word is also used for the act of performing a solo, and sometimes for the performer (more often a soloist).
The plural is 'soli' or 'solos'. In some context these are interchangeable, but 'soli' tends to be restricted to classical music, and tends to refer to either the solo performers or the solo passages in a single piece: it would not often be used to refer to several pieces that happen to be for single performers.
A piece written for a single performer is referred to as a solo, often qualified by instrument, as piano solo or flute solo. These are common for polyphonic instruments such as the piano, organ, harpsichord or harp. Monophonic instruments such as flutes or violins are more often accompanied by piano or other instruments, but there are still plenty of solo works for such instruments, such as the violin partitas and the cello suites of J S Bach.
Solo is not usually part of title of a piece, except sometimes in a phrase such as '... for piano solo'.
A Concerto is a piece written for generally one but occasionally more instrumental musicians and is intendid to be performed accompanied by an orchestra: the distinguished part is referred to as the solo (soli or solos if there are several).
Although there may be passages where only the soloist is playing, generally the solo part is accompanied by the orchestra: its distinctiveness and prominence are what makes it a solo, not whether or not it is played with or without accompaniment.
In a similar way to a Concerto, any ensemble piece may have portions where a single instrumentalist is particularly prominent, and these are often referred to as solos.
The strings in an orchestra are usually grouped in sections, where several players are playing the same music most of the time. But sometimes the music will direct that only one player in the section is to play, or that one player in the section is to play something different from the rest of the section. These are also referred to as solos.
All the types of solo mentioned above in instrumental music have their parallels in vocal and choral music. There are pieces for solo singers, possibly accompanied; there are pieces for soloist and chorus (like concertos, but that word is not usually used); and there are solo passages in choral works.
In many Jazz performances, each number will alternate ensemble sections with solo sections where one performer is playing either completely alone, or with unobtrusive accompaniment from the others. Common examples are the rhythm section of jazz bands, and quiet background music by other wind instruments. Such solos are most often improvised.