The new Signal Chrome app follows the November launch of Signal for Android and an earlier iOS release.
OWS launched a private beta for the desktop in December. The version available to install from the Chrome Web Store has an improved UI, but essentially offers the same end-to-end encryption as the Signal mobile apps, allowing users to carry chats across from their phones to the desktop.
End-to-end encryption is meant to ensure its virtually impossible for anyone but the sender and recipient to view the contents of a message (however, even after WhatsApp implemented end-to-end encryption, the company can be forced by law to turn over backed up messages if they are stored on WhatsApp's servers).
End-to-end encryption also does nothing to protect the metadata around a message, such as details about the sender and recipient, when it was sent and the location it was sent from. ABC Australia provided a neat graphical summary of what can be gleaned using metadata that is now collected under Australia's recently implemented data retention laws.
For now, the Chrome Signal app can only be set up for users who have the Android Signal app. According to OWS, support for iPhone users is coming but there's no timeline for its arrival.