Reading the definition of a gamut, you understand that you cannot have both: accuracy and smooth gradients. 

When you try to maximize the accuracy of color reproduction, gradients are generally not so smooth and vice-versa. 

Rendering intents as defined by ICC are some flavors of reproductions that try to balance accuracy and smoothness.

ICC profile 

A profile from ICC (International Color Consortium) is a binary file format that describes:

• the conversion math between RGB and Lab (also called input profiles),
• or CMYK and Lab (also called output profiles).

The file format is open, but the content inside depends on the intelligence of the profiler software.

An ICC profile is ephemeral, it degrades over time as the printing system degrades. It can also change with weather conditions. Therefore, it is important to update it regularly to maintain good colors.

Rendering intents

You will have different conversions called rendering intents available inside: 

Absolute 

Absolute is the accuracy fanatic. The common colors of the gamuts are not modified. In the case of really different input and output devices (and so gamuts), forget about gradients: the more saturated gradients, the flatter they will be.

Perceptual 

Perceptual is the smoothness fanatic. As the colorimetric intent, it scales the colors based on the media white but also changes the dynamism of out-of-gamut colors allowing to render beautiful gradients in all saturated colors but making the colors falser than false!

Colorimetric 

Colorimetric considers the media white difference and slightly changes all the colors. They are all false but your eyes looking from one print to another (not side-by-side) will adapt to the white background and will not see the difference! It is a compromise between absolute and perceptual rendering.

Black point compensation (BPC) is an equivalent adaptation of dynamism only on the black region to allow better smoothing, especially when used with the colorimetric intent.