How to read & understand C & C++ Standards and the language grammar used therein?

Here's a description of the C++ grammar for expressions, which defines assignment-expression as

assignment-expression:    conditional-expression     unary-expression assignment-operator assignment-expression

In plain English, an assignment-expression can be either a conditional-expression OR a unary-expression, followed by an assignment-operator, followed by an assignment-expression. So, your next question is 'what's a conditional expression' and you consult that part of the grammar, and keep going until you reach the bottom!

So in C++ you can see the operator you referred to can take a 'conditional-expression' as in C, but also an assignment

So with your 'C' hat on, you look at the final a = d part of the operator as an assignment, which the C syntax shouldn't allow. Instead, it would seem some compilers parse the final part of the operator simple as a to to give

 e = (a < d ? a++ : a) = d

But in C++, it's valid to find an assignment there, so the a = d is accepted in its entirety as the final expression, so you get

 e = (a < d ? a++ : (a = d))

You have to refer to what an assignment-expression is. It is defined in the C++03 standard in 5.17/1 [expr.ass] :

assignment-expression:        conditional-expression        logical-or-expression assignment-operator assignment-expression        throw-expressionassignment-operator: one of        = *= /= %= += -= >>= <<= &= ˆ= |=

What it says is that an assignment-expression can be either :

• A conditional-expression
• A logical-or-expression followed by an assignment-operator followed by an assignment-expression
• A throw-expression.

I'm not quoting the grammar definition of everything because that would be pretty huge (most notably because condition-expression covers a lot of things).

So the first thing we see is that an assignment-expression can be a conditional-expression, so we have the C syntax covered. What the C++ standard adds is that the right side of the : can also be something containing an assignment-operator or a throw.

The provided example is good : e = a < d ? a++ : a = d.

Here, the right side of the : is a logical-or-expression (a, because unary-expression is included in logical-or-expression), followed by an assignment-operator (=), followed by an assignment-expression (d, because unary-expression is included in assignment-expression).

Basically, things like:

assignment-expression:    conditional-expression     unary-expression assignment-operator assignment-expression

(as mentioned in some other answers here) are rules used for describing the "grammar" of valid C (or C++). These written-down rules adhere to a certain grammar, too — so I would suggest that you learn that grammar, so that you'll be able to read and understand the rules.

For a start, you could study e.g. the Backus-Naur Form, if you don't already know it. (My link goes to the Wikipedia article on this topic.) While the C++ standard doesn't use Backus-Naur form (IIRC), it's similar enough to get you started.