What does “the details are ‘need to know’” mean here?

Solution 1:

In some places (like a military base, or the intelligence community), some information is classified. To gain access this classified information, an individual needs two things:

• They need to have the proper clearance
• They need to have the need to know

Let's say that I'm in the Army, and I have a SECRET clearance. I can't walk onto a Navy vessel, and demand to see some classified information, just because I have a SECRET clearance. Yes, I have the proper clearance, but I don't have the need to know.

Similarly, if there is TOP SECRET information in my Army unit, I won't get access to that information, either. I may have the "need to know" (in other words, that information may be directly related to my job), but I don't have the proper clearance.

In the case of the script, I don't think the information is classified – I think the character is essentially saying, "You're being nosy; I don't need to tell you that," but using language that a spy would be very familiar with.

Solution 2:

The OED says:

need-to-know, adj. Designating or relating to a principle or policy of telling people only what is deemed necessary for them to know in order to carry out a task effectively.

The phrase seems to have originated in nuclear weapons research in the US:

1951   Science 21 Dec. 656/2   Distribution of scientific reports..is based on a ‘need-to-know’ policy because of security restrictions and the high cost of reproduction and distribution.

1956   Bulletin of the Atomic Scientists XII May 176   What about your definition a little while ago about the need to know? How can you exchange the information, because everybody has to qualify on a need to know?