Effectively they issue a bond bundled with a bunch of options that may be exercised in exchange for giving up ownership of the bond, "converting" it to equity.
This isn't necessarily driven by a view on the equity valuation. It's more often driven by high realized volatility in the equity, which increases the value of the equity optionality. Correspondingly this decreases the value of the fixed income aspect of the bond, which from the issuer's (Twitter) perspective means they pay less in interest.
Note that "Twitter expects to enter into privately negotiated convertible note hedge transactions". This means that they will buy call spreads to help manage the EPS impact of increasing the fully-diluted share count. Realized volatility and the pricing across strikes of the option chain will be affected.
This isn't necessarily driven by a view on the equity valuation. It's more often driven by high realized volatility in the equity, which increases the value of the equity optionality. Correspondingly this decreases the value of the fixed income aspect of the bond, which from the issuer's (Twitter) perspective means they pay less in interest.
Note that "Twitter expects to enter into privately negotiated convertible note hedge transactions". This means that they will buy call spreads to help manage the EPS impact of increasing the fully-diluted share count. Realized volatility and the pricing across strikes of the option chain will be affected.