A color value is only a set of numbers until a profile explains what those numbers mean on a device or under a print condition.
Profiles give numbers meaning
The same RGB or CMYK values can produce different colors on different devices. An ICC profile describes how a particular color space or production condition relates to a device-independent reference.
Assigning and converting differ
Assigning a profile changes the interpretation of existing numbers, so appearance can shift immediately. Converting attempts to preserve appearance while changing the numbers for a new destination. Confusing these commands is a common source of bad color.
Working profiles organize editing
A working RGB profile provides a predictable space for editing and interchange. An output profile predicts a printing condition and controls separation choices such as gamut mapping, black generation, and ink limits.
Soft proof, then hard proof
A calibrated display and correct output profile can simulate many print limitations, but it cannot reproduce paper texture, fluorescence, metallic ink, or every viewing condition. Use a physical proof when the decision matters.