What do the nomodeset, quiet and splash kernel parameters mean?
From this question, about nomodeset:
The newest kernels have moved the video mode setting into the kernel. So all the programming of the hardware specific clock rates and registers on the video card happen in the kernel rather than in the X driver when the X server starts.. This makes it possible to have high resolution nice looking splash (boot) screens and flicker free transitions from boot splash to login screen. Unfortunately, on some cards this doesn't work properly and you end up with a black screen. Adding the nomodeset parameter instructs the kernel to not load video drivers and use BIOS modes instead until X is loaded.
From Unix & Linux, on quiet splash:
The splash (which eventually ends up in your /boot/grub/grub.cfg ) causes the splash screen to be shown.
At the same time you want the boot process to be quiet, as otherwise all kinds of messages would disrupt that splash screen.
Although specified in GRUB these are kernel parameters influencing the loading of the kernel or its modules, not something that changes GRUB behaviour. The significant part from GRUB_CMDLINE_LINUX_DEFAULT is CMDLINE_LINUX
This answer covers acpi, noapic and nolapic:
In general, such boot parameters are not needed unless there is a problem with your BIOS and how it handles these standards, or it just might be old enough where these standards were not fully implemented properly.
ACPI (Advanced Configuration and Power Interface) is a standard for handling power management. Older systems may not support ACPI full, so sometimes it helps to give the kernel a hint to not use it. "acpi=off"
APIC (Advanced Programmable Interrupt Controller) is a kind of feature found on newer systems. The "local" version is called "LAPIC". What this controller can do is be set up to generate and handle interrupts, a signal the hardware uses to pass messages. Again, some implementations of APIC can have problems on older system, and so it is useful to disable it. "noapic" and "nolapic".
Sometimes the APIC is working, but it slows things down by getting in the middle of messages being passed around. This can mess with audio and video processing, for example. Folks might disable it for that reason as well.
Additional parameters can be found here.
These are instructions passed to the kernel during the boot time. In Ubuntu, they are managed by the GNU GRUB (GRand Unified Bootloader).
quiet- this option tells the kernel to NOT produce any output (a.k.a. Non verbose mode). If you boot without this option, you'll see lots of kernel messages such as drivers/modules activations, filesystem checks and errors. Not having thequietparameter may be useful when you need to find an error.splash- this option is used to start an eye-candy "loading" screen while all the core parts of the system are loaded in the background. If you disable it and havequietenable you'll get a blank screen.nomodeset- tells the kernel to not start video drivers until the system is up and running.
There are lots of other boot parameters, such as:
3- starts the system in runlevel 3 (default is 5). If you append this parameter, you will be dropped in a command line environment (runlevel 5 is needed for a GUI).init- indicates the location of the "init" script. This script is the first process started in an Unix-like system, and is responsible for start all other processes. Syntax:init=/path/to/script
These are not "Ubuntu boot options". They are "kernel boot options".
It is not possible to describe all kernel boot options in one answer. Many kernel modules have some kind of options that can be used in grub.
You can easily find what nomodeset does.
Other options can be found too.