I think the この通り means (or, comes from) something like 「この通り、謝ります(だから許してください)。」 "I'm apologizing like this / as you see (so please forgive me)" or 「この通り、お願いします(だから頼みを聞いてください)。」 "I am begging you like this / as you see (so please do me a favor)."
This phrase is used when you apologize someone or ask a favor of someone, and you'd usually say it while lowering your head, or joining your palms together as if in prayer, or maybe doing dogeza..., your word この通り indicating your gesture/action of apologizing or pleading.
Examples:
「本当に申し訳ありません!この通りです!」(I am very sorry! I apologize!)
「ごめんなさい!この通り!」 (I'm sorry! I apologize!)
「許して!この通りだから!」 (Forgive me! I'm begging you!)
「お願い!この通り!」(Please! I'm begging you!)
↓ Though I think people normally bow deeper than this: