It works much like you'd expect: you can ask Alexa to add items to the various lists that you have in your Todoist account, and you can also ask it to tell you everything that's on your to-do list for that day. And Alexa works with Todoist's natural language processing, so you can ask it to add things to your list "tomorrow" or "next Wednesday" and it'll know just what you're asking it for. It's not clear if you'll be able to tell Alexa to add items to specific projects or to-do lists in your account -- they probably get added to whatever your default list is for you to sort out on your phone or computer.
The Echo already has its own to-do list features built into it, but they're obviously not as full-featured as something like Todoist. And integrating with an app like Todoist will help Echo match up with Google's upcoming Home assistant, which knows all about your schedule and to-do lists thanks to its close integration with Google's services. If you have an Echo and Todoist account, you can try this out today -- it'll work for both free and paid Todoist users.