Q:

Name for phrase only understood by those who already know?

I'm having a hard time thinking of an example, except I remember someone making a recursive joke about it once. They explained the meaning of it by using its definition, hence the joke. Something like "An X is only an X for those who already know".
What is the name for this kind of phrase?

A:

shibboleth
noun

a custom, phrase, or use of language that acts as a test of belonging to, or as a stumbling block to becoming a member of, a particular social class, profession, etc

Dictionary.com 
Today, in American English, a shibboleth also has a wider meaning, referring to any "in-group" word or phrase that can be used to distinguish members of a group from outsiders – even when not used by a hostile other group
Probably not what you're looking for, but a fun word nonetheless.

A:

esoteric
adjective
1.
understood by or meant for only the select few who have special knowledge or interest; recondite:
2.
belonging to the select few.
3.
private; secret; confidential.
4.
(of a philosophical doctrine or the like) intended to be revealed only to the initiates of a group

A:

The question in your title doesn't really match what's asked in the body of your question. But a possible answer to the question in your title is jargon.

special words and phrases that are used by particular groups of
  people, especially in their work

The Wikipedia entry for jargon adds to this by saying

The main trait that distinguishes jargon from the rest of a language
  is special vocabulary—including some words specific to it and, often,
  narrower senses of words that outgroups would tend to take in a
  broader sense.

In other words, jargon can include words whose meaning within a group is quite different than the meaning outside that group.

