Therewith means with that thing, or immediately after that. It's an old-fashioned word you'll find in classic books and formal documents, but rarely in everyday conversation.

When a knight in a medieval story draws his sword and strikes therewith, he strikes with that sword. When a contract states that someone agrees to certain terms and accepts all responsibilities therewith, it means the responsibilities that come with those terms.

The word appears in older translations of the Bible and in classic literature. In modern English, we'd usually say “with that” or “with it” instead. You might read that a wizard waved his staff and therewith cast a spell, meaning he cast the spell with that staff or immediately after waving it.

Understanding therewith helps you read older texts, but you probably won't use it much yourself unless you're writing something deliberately old-fashioned or formal. It's like understanding how people used to travel by horse and carriage: useful to know about, even though we use cars now.