The idea of using Kalman gain in EKF SLAM is to figure out how much we trust our motion model and sensor/observation model. As explained in The Extended Kalman Filter: An Interactive Tutorial for Non-Experts - Part 5: Computing the Gain, the Kalman gain can be calculated as,
$$K_t = \frac{p}{(p +r)}$$
where $p$ denotes prediction error and $r$ denotes sensor noise.
Now, if we look into the equation in the image,
$$K_t = \bar{\Sigma_t}H_t^T(H_t\bar{\Sigma_t}H_t^T +Q_t)^{-1}$$
we can see that Kalman gain is calculated using Covariance matrix ($\Sigma$), Jacobian of observation model ($H$) and Sensor noise ($Q$). Comparing with earlier equation, $p$ can be considered equivalent of $\Sigma$, while $r$ can be equivalent of $Q$.
How does $H$ fit in, in this equation? What would be an intuitive explanation?