With the emergence of the Advanced Persistent Threat (APT) attacks, many Internet of Things (IoT) systems have faced large numbers of potential threats with the characteristics of concealment, permeability, and pertinence. However, existing methods and technologies cannot provide comprehensive and prompt recognition of latent APT attack activities in the IoT systems. To address this problem, we propose an APT Alerts and Logs Correlation Method, named APTALCM and a framework of deploying APTALCM on the IoT system, where an edge computing architecture was used to achieve cyber situation comprehension without too much data transmission cost. Specifically, we firstly present a cyber situation ontology for modeling the concepts and properties to formalize APT attack activities in the IoT systems. Then, we introduce a cyber situation instance similarity measurement method based on the SimRank mechanism for APT alerts and logs Correlation. Combining with instance similarity, we further propose an APT alert instances correlation method to reconstruct APT attack scenarios and an APT log instances correlation method to detect log instance communities. Through the coalescence of these methods, APTALCM can accomplish the cyber situation comprehension effectively by recognizing the APT attack intentions in the IoT systems. The exhaustive experimental results demonstrate that the two kernel modules, i.e., Alert Instance Correlation Module (AICM) and Log Instance Correlation Module (LICM) in our APTALCM, can achieve both high true-positive rate and low false-positive rate.