How does “δ:Q×Σ→Q” read in the definition of a DFA (deterministic finite automaton)?

δ is like a mathematical function called the transition function . Something like.

z = f(x, y) 

A function in mathematical defines mapping of elements in one set to another set. In function set of input arguments are called Domain of a function and output is the rage.

[ANSWER]   

In expression "δ:Q×Σ → Q",

× means Cartesian product (that is a set), and → is a mapping.
"δ:Q×Σ → Q" says δ is a transition function that defined mapping from Q×Σ to Q.
Where, Domain of δ is Q × Σ and Range is Q.

Note: Cartesian Product itself a mathematical that all possible order pair (mapping) between two sets.

You can also say:

δ is a transition function that defined mapping between(or say associates) Cartesian product of set of statesQ and language symbolsΣ into set of stateQ. This is abbreviated by δ: Q×Σ → Q

Here, Q is finite set of states and Σ is a finite set of language symbols.

Additionally in any automated you can represent transition function in tree ways.
1. Transition Table
2. Transition graph or say state diagram.
3. Transition function: a finite set of mapping rules. e.g. {δ(q0, a) → q1, δ(q1, a) → q2}
_{All for same purpose define maping}

In DFA. δ:Q×Σ → Q can also be written like δ(Q,Σ) → Q It’s similar to function. In δ function two input arguments are state Q and a language symbol Σ and returned value is Q.

What is meaning of δ(Q,Σ) → Q

Suppose in your set of transition function δ you have an element δ(q0, a) → q1 this means.
If the present state is q0 then by consuming a symbol you can shift to state q1. And the state-diagram for δ(q0, a) → q1:

(q0)---a---►(q1)  

and transition table is:

+----+----+
|Q\Σ | a  |
+----+----+
| q0 | q1 |
+----+----+

and all defines mapping (q0, a) to (q1).

Some authors write δ ⊆ Q×Σ → Q in formal DFA definition that means δ is a Partial function (not defined on full Domain Q×Σ). We can always defined δ on the full domain that is required sometime for example to find complement DFA.
Here(Complement DFA), I wrote two DFAs for the same language one is partial DFA other is complement DFA.