Lexicographic ordering on ${\cal P}(\kappa)$ How is the "lexicographic ordering" (which is supposed to be a total ordering) on ${\cal P}(\kappa)$ defined, where $\kappa$ is any cardinal?
(I apologize if this question is a bit fuzzy.)
 A: Identify $\wp(\kappa)$ with ${^\kappa2}$, the set of functions from $\kappa$ to $2$ by identifying each subset of $\kappa$ with its indicator function. Now let $\preceq$ be the natural lexicographic order on ${^\kappa2}$: if $f,g\in{^\kappa2}$ and $f\ne g$, let 
$$\delta(f,g)=\min\{\xi\in\kappa:f(\xi)\ne g(\xi)\}\;,$$
and set $f\preceq g$ iff 
$$f\big(\delta(f,g)\big)=0<1=g\big(\delta(f,g)\big)\;.$$
This is the easiest way to define it so that it’s clearly a lexicographic order. This is equivalent, however, to saying that if $x,y\subseteq\kappa$, and $x\ne y$, then $x\preceq y$ iff
$$\min(x\mathrel{\triangle}y)\in y\;,$$
i.e., the first element of $\kappa$ on which $x$ and $y$ disagree is in $y\setminus x$.
A: If $(X,\le)$ is any well-ordered set then we can define a linear ordering on the power set $\mathscr P(X)$ as follows: 

For $A\ne B$ we say that $A<B$ if $\min A\mathrel{\triangle} B\in A$ (i.e., if the smallest element of the symmetric difference belongs to $A$).

Since every cardinal is a well-ordered set, this applies to your case. (And I suppose that if the text where you stumbled upon this is related to set theory, then this is the most probable meaning of the lexicographic ordering of $\mathscr P(\kappa)$).
For a random sample of some texts where something like this is used you can try to search for lexicographic "symmetric difference" "set theory" in Google Books.

As Brian M. Scott says in a comment, the opposite direction (i.e. $A<B \Leftrightarrow \min A\mathrel{\triangle} B\in B$) is used more often. (And I am willing to take his word for it.) Lexicographic order is defined in this way also in Joel David Hamkins' answer to your related question on MathOverflow in the case $X=\omega$.
From the results returned by the above Google search, Jech uses the direction which Brian mentions here. (I did not find lexicographic order on $P(X)$ in the newer edition of Jech's book, only for functions belonging to $\{0,1\}^X$.) On the other hand, Halbeisen on p. 109 uses the definition I mentioned above.
It is true that the ordering mentioned by Brian seems more natural. It corresponds to ordering between characteristic functions $\chi_A$ and $\chi_B$. For two functions $f,g\in\{0,1\}^X$ it is natural to say that $f<g$ if and only if $f(a)<g(a)$ where $a=\min\{x\in X; f(x)<g(x)\}$.
