What is the "description" of a Turing machine? I am currently reading about the Halting Problem in my course on the theory of computation and the following was given in my lecture slides 



Now my question is that if $d$ is the description of a Turing machine, what exactly is $d$ from a strictly mathematical point of view? The way that $d$ is written above seems to suggest that $d \in Q$ (i.e. that $d$ is a state of the Turing machine $T$), but I can't be entirely sure.
The description is a string that encodes the formal specification of the machine, comprising:


the set of states,
the start state,
the set of halting states (or, where appropriate, the sets of accepting and rejecting states),
the tape alphabet,
the input alphabet,
the transition function.


Some authors also explicitly include the identity of the blank symbol in the description of the machine; others leave it to convention (e.g., stating that the alphabet will always be $c_1, \dots, c_k$ for some&nbsp;$k$, and $c_1$&nbsp;is the blank symbol).