As soon as you start a single or a meditation from a course, the meditation or the entire course will be downloaded. You can also just tap on "Download" and the download will start, but nothing will be played yet. Please note that meditations will only be downloaded if your device is connected to the internet via wifi or mobile data. If you have a limited amount of mobile data, you may want to consider how many meditations you're going to download without wifi.
Keep in mind that playing a meditation is not live-streaming, meaning that you can only play a meditation after it has been downloaded fully.
Once you have downloaded a meditation, you cannot delete it from your device individually. So if you have limited memory on your device, you should not download all meditations at once ;) If you want to delete the downloaded meditations all at once, just log out. After logging in again, you can choose which meditations you want to download.