Perl, just like any other compiler or interpreter, knows how to read your programs and convert them into a more machine-friendly form for execution. It uses a number of techniques to do this, including using a table-driven parser that is built by a program called YACC (or Bison) by reading a high-level description of the Perl syntax. Here's an excerpt from that description that handles OR (||) and AND (&&) operations (from perly.y):

expr    :       expr ANDOP expr
                        { $$ = newLOGOP(OP_AND, 0, $1, $3); }
        |       expr OROP expr
                        { $$ = newLOGOP($2, 0, $1, $3); }
        |       argexpr %prec PREC_LOW
        ;
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This process builds a so-called "parse tree" where each of the operations is represented by a data structure that points to other data structures.

In a compiler that expected to output to machine code, this would be approximately the same, but it would be followed by a pass that would read the parse tree and output machine code. In Perl, instead of making machine code for execution by a real processor, a somewhat higher-level representation is made that is then interpreted and executed by a little program inside Perl.