The magic term is "operator precedence", it determines the order of execution or your atomic expressions.
A = B or C;
# as "=" has higher precedence than "or" it binds it's
# arguments "tighter", so this is equivalent to
(A = B) or C;
# so your expression is a disjunction
# which executes the left operand
(A = B)
# being an assignment, which returns B in the end
# and if that's false, the disjunction (or)
# returns C, which is irrelevant, because that's in void
# but you want
A = (B or C)
# because that's an assignment, an assignment
# evaluates the right operand first
(B or C)
# which itself is a disjunction again and works as described
# above, returning B if true, otherwise C
# and that is then assigned to A, which must be an lvalue
# that means in Perl
my $page = ( $cgi->param("page") or "login" );
# or by using the high-precedence-OR "||"
my $page = $cgi->param("page") || "login";
# because "||" has higher precedence than "="