Before we get too deep into Docker itself, let us also cover some of the current competitors in broad strokes and see how they differ from Docker itself. The curious thing about almost all of them is that they are generally a form of abstraction around Linux control groups (cgroups) and namespaces that limit the use of Linux host's physical resources and isolate groups of processes from each other, respectively. While almost every tooling mentioned here provides some sort of containerization of resources, it can differ greatly in the depth of isolation, implementation security, and/or the container distribution.
The competition
rkt
rkt, often written as Rocket, is the closest competing application containerization platform from CoreOS that was started as a more secure application container runtime. Over time, Docker has closed a number of its security failings but unlike rkt, which runs with limited privileges as a user service, Docker's main service runs as root. This means that if someone manages to break out of the Docker container, they will automatically have full access to the host's root, which is obviously a really bad thing from an operations perspective while with rkt, the hacker would also need to escalate their privilege from the limited user. While this comparison here isn't painting Docker in great light from a security standpoint, if its development trajectory is to be extrapolated, it is possible and likely that this issue will be heavily mitigated and/or fixed in the future.
Another interesting difference is that unlike Docker, which is designed to run a single process within the container, rkt can run multiple processes within a container. This makes deploying multiple services within a single container much easier. Now, having said that, you actually can run multiple processes within a Docker container (we will cover this at a later point in the book) but it is a great pain to set that up properly but I did find in practice that the pressure to keep services and containers based on a single process really pushes the developer to create containers as true microservices instead of treating them as mini VMs so don't consider this necessarily as a problem.
While there are many other smaller reasons to choose Docker over rkt and vice versa, one massive thing cannot be ignored: the rate of adoption. While rkt is a bit younger, Docker has been adopted by almost all big tech giants, and there doesn't seem to be any sign of stopping the trend. With this in mind, if you need to work on microservices today, the choice is probably very clear but as with any tech field, the ecosystem may look much differently in a year or even just a couple of months.
System-level virtualization
On the opposite side, we have platforms for working with full system images instead of applications like LXD, OpenVZ, KVM, and a few others. They, unlike Docker and rkt, are designed to provide you with full support for all of the virtualized system services but at the cost of much higher resource usage purely by its definition. While having separate system containers on a host is needed for things like better security, isolation, and possibly compatibility, almost the entire use of these containers from personal experience can be moved to an application-level virtualization system with a bit of work to provide better resource use profile and higher modularity at a slight increase of cost in creating the initial infrastructure. A sensible rule to follow here is that if you are writing applications and services, you should probably use application-level virtualization but if you are providing VMs to the end user or want much more isolation between services you should use a system-level virtualization.
Desktop application-level virtualizations
Flatpak, AppImage, Snaps, and other similar technologies also provide isolation and packaging for single-application level containers, but unlike Docker, all of them target the deployment of desktop applications and do not have as precise control over the container life cycle (that is starting, stopping, forced termination, and so on) nor do they generally provide layered images. Instead, most of these tools have nice wrapper Graphical User Interfaces (GUIs) and provide a significantly better workflow for installing, running, and updating desktop applications. While most have large overlaps with Docker due to the same underlying reliance on mentioned cgroups and namespaces, these application-level virtualization platforms do not traditionally handle server applications (applications that run without UI components) and vice versa. Since this field is still young and the space they all cover is relatively small, you can probably expect consolidations and cross-overs so in this case it would be either for Docker to enter the desktop application delivery space and/or for one or more of these competing technologies to try to support server applications.