Exactly what is a "third party"? (And who are the first and second party?)

These terms are well defined in English when talking about grammar (English grammar or another language's).

• First person corresponds to the pronouns "I" and "we"; "me" and "us" (so a book written in the first person is a story told by the central character - "I did this" as opposed to "Smith did this").

• Second person corresponds to the pronoun "you".

• Third person corresponds to the pronouns" he", "she", "it" and "they"; "him", "her" and "them".

So "third party" just means not you or me, but them.

If you are developing software for a client, then there is a contract between you/your company, and the client/their company. These are the two parties to the contract. Anyone else, not bound by the contract, is a third party. It's used wherever a contract exists between two parties to mean anyone not bound by the contract.

There is no fixed meaning to which of the two parties is 'first' and which 'second', usually you will think you're the first party, and the client the second, whereas the client will think they are the first party and you the second, in a similar fashion to first, second and third person I/he/they.