Can you explain what this means? What does borrow against your stock mean

At most brokerages, etrade for example, you can take out a loan with what you own as collateral. https://us.etrade.com/bank/line-of-credit

Got it, but I still don't understand what "And if you want some leverage, borrow against your stock with a credit line." means. How does this increase leverage?

By borrowing against your securities you have more cash to invest. You've put a multiplier on the amount you can invest. That's leverage. However, you have to pay back the loan with fees and interest. This increases risk because you could end up owing money rather than just having none if the securities crash.

Options provide more leverage than margin.

Options decay though. They can be a very good way to increase your leverage and can be awesome to increase your exposure especially if you get into more complicated strategies, but for pure long term index investing on margin for leverage is better.

The interest rates are very low right now and the risk, while still obviously higher than non leveraged investing, is much lower than with options. That's only true if you invest in the main (slower moving) indexes though, being leveraged on individual stocks can be much more risky.

Writing OTM calls on index ETFs you own can be a good way to increase your return with almost no risk though (expect the risk of limiting your upside).