Let's look at examples of what happens if we measure our specimen (apple) using a spectrophotometer
under Standard Illuminant

(example 1) and Standard Illuminant A (example 2).
In example 1,

is the graph of the spectral power distribution of Standard Illuminant

and

is a graph of the spectral reflectance of the apple.

is the spectral power distribution of the light reflected from the specimen (apple) and is the product of

and

.
In example 2,

is the spectral power distribution of Standard Illuminant A and

is the spectral reflectance of the specimen (apple), which is the same as in Example 1.

is the spectral power distribution of the light reflected from the specimen (apple) and is the product of

and

.
If we compare

and

, we notice that the light in the red region is much stronger in

, meaning that the apple would appear much redder under Standard Illuminant A.
This shows that the color of a subject changes according to the light under which it is viewed.
A spectrophotometer actually measures the spectral reflectance of the specimen;
the instrument can then calculate numerical color values in various color spaces
using the spectral power distribution data for the selected illuminant
and data for the color matching functions of the Standard Observer.