Name: The internal name

Prefix: For items. The prefix that's added to the item's displayname if it has this affix on it. (Example: "Healthy" is a prefix in "Healthy Leather Pants.")

Suffix: Same as prefix. I'm not sure, but I believe this is unused in TL2. The vanilla affixes all seem to use prefix even when they are grammatically suffixes. (You might try this out to see if it even works. And post your findings.)

Rank: I believe this is the priority for this affix's prefix/suffix to appear in the displayname versus the prefixes/suffixes coming from other items. (Example: If your leather pants have both +hp and +electric damage, the rank on the affixes determines whether the displayname ends up as "Healthy Leather Pants" or "Shocking Leather Pants")

Play Hit Particle: I believe this controls whether the light burst and sound effect displays when the enchanter adds this to an item.

High Quality: Controls whether the affix counts as a "strong enchantment" that gets the special light burst and sound effect when an enchanter adds this to an item.

Spawn range: On what level units can this affix spawn.

Duration: Provides overrides duration for the effects in this affix. Some over-time effects behave differently if duration is set in both places.

Weight: Used for spawn chance. The odds of a particular affix spawning are that affix's weight divided by the sum of all the weights of affixes that are eligible to spawn (i.e. meet the level range, unit type, and difficulty level requirements). If zero, this affix will never spawn randomly and must be manually assigned.

Slots occupy: Each grade of item has a certain number of "slots" for affixes to go in(defined in globals.dat). Each affix takes up a certain number of slots. When an item is generated, unless it already has affixes assigned to it, it keeps rolling affixes until all its slots are full.

Unittypes: What unit types the affix is allowed to spawn on.

Not Unittypes: What unit types the affix is not allowed to spawn on. "Not unitypes" takes precedence over "unittypes."

Enchanters and socketables work funky -- you need to include the unit types it can apply to in "unittypes," and also exclude those same unittypes in "not unittypes," and include the enchanter's unit type or "socketable" in "unittypes." Somehow the game understands this as saying "never spawn this affix on these item types, but do let enchanters/socketables add it to these item types." Your picture provides an example.

Difficulties allowed in: Which difficulty levels will this affix operate in. If this box isn't checked, the affix does nothing in that difficulty level. I've used this to make monster skills that are balanced differently for different difficulty levels.

Oh, I missed this information. Thanks Chthon, now this has become clearer to me. 
This should be Wiki! 

I found one wrong affix! 
GEMS\GEM_UNIQUE_PERCENTLIFESTEAL
It contains

[NOT_UNITTYPES]
<STRING>UNITTYPE:ARMOR
<STRING>UNITTYPE:TRINKET
[/NOT_UNITTYPES]But it should be
[NOT_UNITTYPES]
<STRING>UNITTYPE:ARMOR
<STRING>UNITTYPE:TRINKET
<STRING>UNITTYPE:WEAPON
[/NOT_UNITTYPES]Because of this error, this affix can spawn in weapons.