Alexa on your desktop or laptop works much the same way it does on your Echo smart speakers: you ask Alexa what the weather is, tell it to control your smart lights, and play some music from Amazon Music — if you subscribe to that. If your laptop or desk has support for waking up for Cortana commands, you can also use Alexa to wake your PC up for commands.
Speaking of Cortana, Amazon and Microsoft collaborated on integrating the two smart assistants. Users could (and still can) launch Cortana, then ask Cortana to give Alexa a command. That’s not going away, but with Alexa available as an app that anyone could download on any laptop or desktop, it’s hard to imagine that feature will be used much going forward. The same integration let Alexa users ask to give Cortana a command, but it’s hard to imagine anyone actually doing that.
Amazon notes that the experience of using Alexa on a PC isn’t too different compared to using it on other platforms, but it’s planning to add PC-specific capabilities to the voice assistant in early 2019. It’s anyone’s guess as to what those are, but we should find out soon enough.