Question

As far I know, the my operator is to declare variables that are truly lexically scoped and dynamic scoping is done using the local operator to declare a variable.

Can any one describe them in brief?

Answer 1

local($x) saves away the old value of the global variable $x and
assigns a new value for the duration of the subroutine which is
visible in other functions called from that subroutine. This is done
at run-time, so is called dynamic scoping. local() always affects
global variables, also called package variables or dynamic variables.

my($x) creates a new variable that is only visible in the current
subroutine. This is done at compile-time, so it is called lexical or
static scoping. my() always affects private variables, also called
lexical variables or (improperly) static(ly scoped) variables.

Take a look at the Perl-FAQ’s: