Country singers are always talkin' about how they've got soul..?

It's a genre of music.

Colloquially: authenticity, style, or passion. Used almost exclusively in expressions similar to "he's got soul," often used to refer to individual (e.g. improvisational) expression in music styles such as jazz.

Also, a harmonically simple, often syncopated, style of music made by black people such as James Brown, usually played by small groups, though occasionally involving horn sections, related to funk and rock and always having vocals. This music is claimed to embody the above characteristic.