Colour Space
A defined set of colours, described by primaries, a white point and a transfer function, within which numerical colour values have a specific meaning.
In depth
Without a colour space, the value 255,0,0 means only 'as much red as this device can make' — which differs on every device. A colour space anchors those numbers to real, measurable colours, making the same file reproduce consistently. Choosing one is a trade between the range of colours available and how widely the file will be understood.
Examples in practice
The same RGB numbers appear as a muted red in sRGB and a far more saturated one in ProPhoto RGB.