The EC is typically a small microprocessor sitting on your motherboard, often implemented in the same hardware as the keyboard controller. It shares a lot in common with the keyboard controller - on PCs it'll usually appear in system io space, with one register for writing a command or reading a status, and a second register for passing data back and forth. There's 256 registers available, so a typical interaction might be to write the READ command (0x80) to the command register, write the EC register address to the data register and then read back from the data register to get the EC register contents.
The embedded controller will often be responsible for tracking information about the hardware, such as the temperature. Attempting to read the temperature through ACPI will execute an ACPI method - in the case of the temperature being monitored by the embedded controller, this method will attempt to read from an EC register. The EC driver then performs the read and returns the result, which gets converted into decidegrees kelvin and passed back to whatever made the temperature query.
But, as mentioned above, the EC also generates events. These may be in response to a user initiated event like a hotkey press, or may be triggered by some change in hardware state like a thermal trip point being passed. The embedded controller will then raise a GPE.
Unlike normal GPEs, the EC GPE is not handled by looking for a _Lxx or _Exx method. Instead, the ACPI tables provide information about the GPE that the EC is using. This may be in the form of a _GPE definition in the EC object in the main ACPI tables, or alternatively may be provided in an ECDT (Embedded Controller Descriptor Table), an optional table that provides all the EC information. In either case, the OS knows which GPE will be triggered by the EC. It then installs a handler that will be called whenever the EC raises that GPE.
Things get a touch confusing at this point. The first thing this handler does is read the command byte, which functions as a status byte on reads. It then checks whether the SCI_EVT bit is set. This informs the system that the GPE was in response to a hardware event, and so the EC handler writes a query command to the EC command register and then reads back a value between 0 and 255 from the data register. This is then mapped to a _Qxx method, with xx representing the number of the EC event read from the data register. Like the _Lxx and _Exx methods, the _Qxx method is then executed.
The problem with all of this is that the EC isn't that fast. When a byte is written to it, it's necessary to read back the status byte and check whether the IBF bit is set. This is set when the OS writes a byte to the data register, and cleared once the EC has processed it. The straightforward way to deal with this is to poll the status byte until the bit is cleared, and then write the next byte, but polling is slow and wastes CPU time. The EC can instead be set to interrupt mode, where it'll fire a GPE when the IBF bit clears.
The EC has one additional function. The ACPI spec allows for an i2c bus to be implemented through the EC, with EC registers mapping to i2c registers. The observant among you will realise that this means that there's an indexed access protocol being implemented on top of indexed access hardware, which is more layers of indirection than seem sane. For additional humour, this is usually only used to add support for ACPI smart batteries. ACPI batteries are generally abstracted behind a set of ACPI methods that provide information. Smart batteries instead speak i2c directly to the OS for no real benefit. Linux handles these devices fine, and while the chances are you probably don't have one, the chances are also that if you do you haven't noticed.
The final quirk of ACPI events is that there's yet another means of delivering events. The term "fixed feature" is used to describe an ACPI device that isn't described in the ACPI tables. A power button may be implemented as a fixed feature device rather than a normal ("control method") device. This is indicated by a flag in the fixed feature block. Hitting a fixed feature power button will generate an ACPI interrupt, but no GPE. Instead the OS has to read the fixed feature block and note that the power button flag is set there. It then notifies userspace appropriately. Sleep buttons can also be implemented this way, but other devices will be in the normal ACPI tables and will generate either GPEs or EC events.
 On my laptop, these are ports 0x62 and 0x66 - compare to the keyboard controller's use of ports 0x60 and 0x64
 As directly as indirection via the EC can be...