Cantabile can have several slightly different meanings depending on the context. In general, it is a word that indicates music that is to be performed in a very flowing, melodious and lyrical style. In this sense, it is a type of musical direction. An Italian term, the direction actually is borrowed from the Latin cantabilis, which means "worthy to be sung." The root Latin is cantare, which means "to sing."
Composers first started to use cantabile in their music in the early 18th century. To composers of that period, the term translated to legato performance, although tempo was measured. Later on, the term indicated that the performer should draw one line out. In either case, a fundamental principle was that, in order to have a singing quality, the performer needed to execute the music with expression, flexibility and an overall sense of naturalness. The idea was to convey as much humanness and drama through the line as possible, even if the music was not for the voice.
Cantabile appears in music in two major ways. The first way is paired with a tempo marking at the beginning of the score or individual part, such as "largo cantabile." Used in this manner, the term indicated the performer should take a singing approach at a specific speed to the entire work, or at least to the first section of the music until another performance direction appeared.
The designation can also can show up in sheet music as an independent musical direction. For instance, if the composer wanted one section of line to have a little more sweetness or connection, he might write the word where he wants the performer to approach the music in that way. Composers do not always write additional directions to indicate where the cantabile section is to end, however, so musicians have to use some experience to judge where to move away from the cantabile style.
In some instances, cantabile refers to the first half of a double aria. The freedom of performance assumed with this direction was especially suited to this form because it contrasted so well with the second half of the aria. Normally, the second half of the double aria was a more rousing cabaletta.
Less commonly, people who say "cantabile" are referring to specific musical works that have the term in the title. Sometimes they pair the term with the composer of the work, rather than listing the specific title. For instance, they might say something such as "The Tchiakovsky cantabile is extremely beautiful."