What is the meaning of the sum of kernel components in digital image filtering?
Considering an LTI filter impulse response (aka filter kernel) $h[n_1,n_2]$, then its frequency response will be

$$ H(\omega_1,\omega_2) = \sum_{n_1} \sum_{n_2} h[n_1,n_2] e^{-j \omega_1 n_1}e^{-j \omega_2 n_2} $$

When an image is filtered, its average brightness is mostly affected by the DC response of $h[n_1,n_2]$, which is given by $H(0,0)$. When you want the brightness not to change after filtering, then you set $H(0,0) = 1$, which means that

$$ H(0,0) = \sum_{n_1} \sum_{n_2} h[n_1,n_2] e^{-j 0 n_1}e^{-j 0n_2} = \sum_{n_1} \sum_{n_2} h[n_1,n_2] = 1 $$

Which shows that the sum of impulse response (aka filter kernel) samples is one.