Part 1: An express explanation
Before we start talking about the details on each platform. Let's start by looking at why you should care by talking about ways to handle external events and I/O operations.

Ways to handle I/O events.

I/O has one important property: it takes time. And it's not our CPU or program that's busy, it's some other computer, a disk or some other peripheral that we need to wait on.
Now, to do most I/O operations, we need to go through the operating system. I/O operations are per definition dependent on resources which our operating system tries to abstract over, whether it's the disk drive, the network card or other peripherals. Now, especially in the case of network calls, we're not only dependent on our own hardware, but we depend on resources that might reside far away from our own, causing a significant delay.
If all this is relatively new to you, I have written a whole book about basic concurrency. Especially two chapters should be interesting to read before you go on. Interrupts, Firmware and I/O and Strategies for handling I/O.

Blocking I/O

When we ask the Operating System to perform a blocking operation it will suspend the thread that makes the call (it will stop executing code, store the CPU state and go on to do other things). When data arrives for us through the network, it will wake up our thread again and let us resume.

Non-blocking I/O

Unlike a blocking I/O operation, the Operating System will not suspend the thread that made an I/O request, but instead give it a handle which the thread can use to ask the operating system if the event is ready or not (to follow our network example, if data has arrived for us or not).
When we ask the operating system using our handle we call that pollingsince we are actively asking for a status.
Non-blocking I/O operations gives us as programmers more freedom, but as usual, that comes with a responsibility. If we poll too often, like in a loop, we will occupy a lot of CPU-time to just ask for an updated status which is very wasteful.

Why not use blocking I/O and many threads?

You're right, that's actually a really good idea and an absolutely acceptable solution for many tasks. However, when you have many small tasks you need to handle and a lot of I/O, you'll get into some issues using this approach. An example of one such system is a web server. The tasks are usually very small, and each task spends a proportionally large amount of time waiting compared to actually doing work. Let's consider some downsides of using one thread per task in such a system:

Each thread has a huge stack

Even though this can be configured on some systems, the stack each thread uses is much bigger than what we might need waiting for small tasks. This results in each waiting thread occupying a lot of memory that simply goes unused and you'll hit a bottleneck on memory pretty fast.

Context switches and overhead

Even though the OS is pretty good at running many threads concurrently context switches has some overhead, the real cost lies in creating new threads which involves a lot of bookkeeping and setup related to security. We could alleviate this slightly by using a thread pool. A thread pool is still not optimal in the typical use case when we have a huge amount of small tasks which are mostly waiting, or if the number of tasks (the load) varies a lot.

Epoll/Kqueue/IOCP

These methods let us hook into the OS in a way in which we can wait for many events. Instead of being limited to waiting on one event per thread, we can wait for many events on one thread. This lets us avoid one of the biggest drawbacks of using one thread per event, which is all the memory that is occupied and the overhead of continuously spawning new threads. Now we only have one thread waiting for many tasks.
These methods have in common that they are a sort of blockingI/0. If we only register one event to the epoll/kqueue/iocp event queue and wait for it, it will be no different from using blocking I/O. The advantage comes we can have a queue that waits for hundreds of thousands of events with very little wasted resources.

Readiness based and completion based models

The most significant difference in the way epoll/kqueue and IOCP work is that they use two different models:

Readiness based models

Both Epoll and Kqueue is what we call "readiness based". This means that they'll give a notification when an operation is ready to be performed. An example of this is when data is ready to be read into a buffer.

Completion based models

IOCP is an abbreviation of Input/Output Completion Ports. As the name implies, this is a completion-based model which means that we get a notification when an operation has happened. An example of this is when data has been read into a buffer.
While these differences seem small, it has quite an impact on the difficulty of creating a cross platform event queue as we'll see in part 2 of this book.
If you follow along on the next three chapters, you'll see how these work in practice.
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