One more for 2011

[Tirea Aean]

it is mostly used in 2 ways, as explained in the blog:

appositives - My friend, John. (alu translates to comma here)

rephrasing explanations - he shot a yerik from the top of home tree, that is to say, He is an extremely good hunter. (alu translates to ",that is to say" here)

[Toruk Makto]

Well crap. That is kind of hard to boil down to something concise. 

[Tirea Aean]

well, on his blog, he defined it as

alu |

CONJ |

'that is, in other words; used for apposition'

EDIT: Then he had this to say:

ALU
Used mainly for nouns or noun phrases in apposition—e.g. 'my friend Amhul,' 'Eytukan, leader of the Omaticaya,' 'Eywa, the Great Mother,' etc. It comes from a + lu, with a fusing of the two words into one and a change in stress to the first syllable. Example:

Tskalepit oel tolìng oeyä tsmukanur alu Ìstaw. 'I gave the crossbow to my brother Istaw.'

You can also use alu conversationally as an "explainer," in the sense of "that is to say" or "in other words":

Txoa livu, yawne lu oer Sorewn . . . alu . . . ke tsun oeng muntxa slivu. 'Sorry, but I love Sorewn . . . in other words, you and I cannot marry.'

DOUBLE EDIT: This post is pretty much superfluous, as Ikran Ahiyik already posted all this a few posts above.

[Irtaviš Ačankif]

I usually think of "alu" as "which is", since "a lu" is "which is."

Fìfkxen alu FÌ'u lu ftxìlor; tsafkxen alu TSA'u ngati tspang.

Literal translation: This plant which is THIS one is delicious, that plant which is THAT one kills you.

If I were to say that sentence though, I would just throw away the fì and tsa prefixes because they don't take stress and make the sentence sound weird:

Fkxen alu FÌ'u lu ftxìlor; fkxen alu TSA'u ngati tspang.
Literal translation: The plant which is THIS one is delicious, the plant which is THAT one kills you.

[Blue Elf]

I usually think of "alu" as "which is", since "a lu" is "which is."

But then what would be rule when to use "a lu" and when "alu" - if they mean both the same?

Alu means "that is" or " by other word"

See this post, how Le'eylan explain this (my question is one post above)

[Tanri]

But then what would be rule when to use "a lu" and when "alu" - if they mean both the same?

The meaning is the same but the grammar not.

Srake oeyä tsmukan alu Ìstaw smon ngar? - Do you know my brother Ìstaw?
Alu is used to connect two nouns in apposition, or as a "explainer".
In this example it is literally "my brother which is Ìstaw".
Note that alu do not alters the grammatical structure of the sentence, it just connects two nouns. If you remove "alu Ìstaw", nothing happens to the rest of the phrase.

Sawtutel pxìm peng aylì'ut a lu stxong. - Humans often say words that are strange.
The meaning appears to be the same, but grammar is completely different.
"a" is connecting attributive subordinate clause "lu stxong" to the noun aylì'u, thus "a" and "lu" are grammatically independent.
What makes us think that they form one big conjunction, is the fact that they are used to connect attribute (adjective) to the noun.