A Kalman filter will give you the "best guess" for some state (x) at the current timestep (k). This estimate often has some lag in it, likely because you have some incomplete information that you couldn't model. Sometimes we care about the previous states (e.g., x_k-1). But if we just save these states and refer to them, we're not getting the most out of our data.
The Kalman Smoother can be used to go back and update these past values with all the samples up to the current time. To update your previous measurements, you need to save the state of your filter at every timestep (x_k) and its associated covariance matrix (P_k). You can then apply Kalman Smoothing to reprocess previous data and update it with all current information. This will often remove the phase delay that you would otherwise observe in your estimate.