acpi=off or noacpi
Disables the "Advanced Configuration and Power Interface" or ACPI which is used for power management in general (Fan speeds, sleep states...). In some cases like running the installer from a Live USB or booting a laptop it is needed for compatibility with the motherboard and how it handles/mishandles ACPI. Just in case you are wondering, the difference between acpi=off and noacpi is that acpi=... can accept more values. For example acpit=force,irq.
noapic
Disables the "Advanced Programmable Interrupt Controllers" which is used to resolve hardware conflicts for interrupts. The effects of using a combination between noacpi and noapic depends on the hardware. In some cases, disabling both will solve booting problems, in others it will create problems. Suggestions are that you try one at a time.
nolapic
Disables the "Local Advanced Programmable Interrupt Controler" which applies to newer CPUs and they are handled. nolapic is commonly used when you are using old hardware. Many times even withnoapic`.
edd=on
Enables the "Enhanced Disk Drive" service which is used by VERY old motherboards to provide support for hard drives, specially ones that go beyond the 32GB barrier, which by todays standards is like the size of a normal flash drive. Anyway, if you have an old motherboard and a HDD bigger than 32GB, then use edd=on.
nodmraid
Disables the "Device Mapper RAID" which is used for everything related to RAIDs. Not recommended if you want to use RAIDs.
nomodeset
Disables the video from using modesets which are used for example for better resolutions and graphics. If you are using an old video card, old monitor or both, then activate this mode.
Free Software Only
Simple eliminates all options to install restricted drivers, codecs or in general any proprietary software. This is all for legal purposes and/or if you want to have a 100% free software environment, but note that you will not be able to listen to MP3 songs, use your Nvidia or Ati card to full potential or watch H264 or Flash videos. You will need to install them afterwards when you finish with the Ubuntu install process.
For more information here are 2 good links about the Kernel parameters:
You can see all Kernel parameters here: http://fxr.watson.org/fxr/source/Documentation/kernel-parameters.txt?v=linux-2.6
Ubuntu used parameters are here: https://help.ubuntu.com/community/BootOptions#Common_Kernel_Options