Math behind the Genetic Relationship Matrix
This expression is a mean
$$\frac{1}{m}\sum_{i=1}^m ...$$
($m$ is the number of SNPs) of the ratio
$$\frac{numerator}{denominator}$$
where the numerator is a covariance
$$(a_i-C)(b_i-C)$$
and the denominator is the expected heterozygosity (it is also the variance of binomial distribution with n=2)
$$2p_i(1-p_i)$$
Therefore, it represents how much do two individuals covary $(x_{ij})(x_{ik}-p_i)$ respectively to what is expected on average $2p_i(1-p_i)$ averaged over all SNPs $\frac{1}{m}\sum_{i=1}^m...$, where $m$ is the number of SNPs.
It is a relative measure (relative to the expected heterozygosity) of covariance between each individual (averaged over all SNPs).
Does it help?