The Ninth Doctor said it was a gift of The TARDIS, its translation circuits that allows all that has it to understand alien languages. I was rewatching The Christmas Invasion and was wondering does it allow everyone to understand or just people that travel in The TARDIS, or is it a sort of AOE? How is it decided?

The way I understand it, is that it translates for the Doctor and companion, and then makes them sound to the aliens as though they are speaking there language, even apparently going as far as to manipulate everyone's perception to make it seem as though everyone else's mouths are moving as they should with what it appears they are saying.

It's usually limited to the Doctor and his companions but as can be seen in The Christmas Invasion others can be included as well.

Since the translation gift only works when the Doctor is conscious who is included is probably down to him as well.

In many foreign countries DW is totally re-dubbed with their native language on broadcast, so the TARDIS translates to the viewers in other languages too.

The one thing that bothers me about this is that it doesn't do all languages; The Doctor still speaks in that "Ho bo ro so mo ho" fashion to the Judoon. Why doesn't the Tardis translate that language?

I don't know where I got this from but I believe it's because the Judoon brain function is so simple that it cannot respond to the telepathic matrix. The Judoon's own translation device is of course electronic

Well, it works for me. I have always understood the aliens (except the Judoon).

RTD states as such as in The Writer's Tale. A cut line in the Stolen Earth would have explained it on screen. Basically, as you said the Judoon are so thick the TARDIS regards their language as little more than animal noise.

The poor TARDIS must have worked so hard during the Davison years when there was four inhabitants all potentially speaking different languages. .

It doesn't explain how people who never set foot in the Tardis could communicate with aliens. I'm sure there's been examples of that.

How old is this explanation in Doctor Who? When was it first mentioned?

I vaguely remember Jo Grant being revealed as being under the Master's control when she asked the Doctor about how she could understand alien languages. The Doctor answered and later explained he knew she was under the Master's spell as it would never have occurred to her to ask the question. (From memory. I may have got that wrong!)

Was RTD inspired by Douglas Adams's Babel Fish? That, in turn, was inspired by his need to comically "explain" how, in most science fiction, newly contacted aliens were invariably able to speak perfect English.

The language problem was usually ignored for the sake of dramatic pace and variety. When it was addressed it was usually via some dubious techno-babble, such as Star Trek's Universal Translator.

It was Sarah Jane not Jo and it wasn't the Master and it was Italian rather than an alien language (rest is correct )

Everyone in the world speaks the Queen's English. The just pretend not to. Its the same in space.

You are, of course, absolutely correct. English is the universal language, literally.