Songwriting is, in it's most basic definition, the act of writing a song (obviously).
But the word doesn't even have to apply to that specifically; the term songwriting is often used to describe the writing of individual song parts, such as the guitar or vocal melodies. Strictly speaking, songwriting and composing are interchangeable words. They do, after all, denote the exact same thing. But the connotation here is radically different. While composing is seen as the province of classical musicians who actually record their compositions onto sheet music, songwriting is far more informal, the work of rock, pop, folk or country musicians who may take some notes, but generally commit everything they've written to memory.
The actual act of songwriting varies from musician to musician. Some say that solo musicians have the easiest time of songwriting, writing whatever they want without having to clear it with a band or partner. But solo musicians also carry the burden of songwriting wholly on themselves. When they lack inspiration for a certain part or harmony, they don't necessarily have someone to fix the songwriting block for them. Musicians songwriting as part of a group, however, are given the luxury of using their band-mates as a sounding board.
In many band situations, no one person is responsible for all the material; someone will write a part, which is then elaborated on by the others. For instance, a guitarist may come to band rehearsal with a solid verse and chorus. The drummer may then write a series of parts based on the guitarist's part, the bass will write based on the drums, and keyboards or other instruments will write based on that core grouping. Vocal melodies are frequently the province of the vocalist alone, and while every musician has some say in what the other musicians are playing, the songwriting from instrument to instrument is largely the decision of the individual musicians. There are no strict rules to songwriting; whatever works for the musicians in question becomes the norm.
