Container security is a deep subject area and in itself can fill its own book. Having said this, we will cover some of the high-level concerns and give a starting point to think about this area.
In the A brief overview of containers section of Chapter 1, Introduction to Kubernetes, we looked at some of the core isolation features in the Linux kernel that enable container technology. Understanding the details of how containers work is the key to grasping the various security concerns in managing them.
A good paper to dive deeper is NCC's Whitepaper, Understanding and Hardening Linux Containers (you can refer to more details about this in point 1 in the References section at the end of the chapter). In section 7, the paper explores the various attack vectors of concern for container deployments, which I will summarize (you can refer to more details about this in point 1 in the References section at the end of the chapter).