A specification -- for any technical device or part thereof -- is a document that describes what it does do, or what it should do.
Note that in some situations a specification for a part will be called a "requirements document". They're not exact synonyms: if it's built and you're selling it, you'll almost never call the document that describes it the "requirements", while if you're in a really formal process where the whole document gets written first and then design starts, it'll most likely be called "requirements". But within those extremes, there's a lot of overlap.
Depending on the design process used, the specifications may be written before the board is designed (i.e., the "pure" waterfall model), or the specification may be written as the board is designed (i.e., the "spiral" model, aka "agile"), or they may be written only after everything has been made to work and someone wants to sell it (i.e. the "make sure your resume is current" model).
Even in pure waterfall models, the board won't exactly match the specification -- when you're designing a board to specification you generally try to exceed specification in every way, so that when you fall short of your own self-imposed mark you still exceed the customer's required specification.
Specifications can be formal, informal, loose or tight. In general, a specification specifies all the important parameters of the part. For a circuit board these may include:
- What the board actually does (this is a good one to include).
- The physical envelope ("space claim") that the board fills, and perhaps cannot grow beyond.
- It's weight
- The mounting features of the board
- The connectors on the board, and possibly their locations
- The power supplies needed by the board, and usually the current draw from each
- The expected inputs and desired outputs.
- Aspects of the environment in which it is expected to work, and survive (i.e., temperature, humidity, vibration levels, shock, vacuum if it's a space application, radiation, etc.)
- Electromagnetic compatibility specifications, both susceptibility and what it can or cannot generate.
"Drafting" is just another word for composing a document, usually leaning toward the initial phases, and possibly the work you need to do to make sure all the details are correct. So if you're "drafting a specification" you're running around making sure that you're asking for something that's both possible and that will make you happy when you're getting it.
Depending on whether the document is going to be internal or part of a contract, you may be trying to dot every 'i' and cross every 't', or you may just jot something down on a napkin -- but usually if you're "drafting" it, you'll be writing it as if it really matters that it be adhered to, and depended upon.