Your account still exists in iCloud so it can be re-used in the future if you want to ever do so. This is important as each device can only create a maximum of three iCloud accounts.
If you want to delete all your data from the account, you can do so as follows:
First go to Settings>iCloud on your device and confirm that everything is turned to Off, and that you are not syncing any data with iCloud before proceeding. (If you are, when you delete the data from iCloud it will also be deleted from your device and it will be lost.) When you turn these off, you will be given the option to keep the data on your device.
To delete your contacts, go to iCloud.com from your computer, log into your iCloud account and open Contacts, click on All Contacts on the left, to the right click on any single contact to select it, click on the Actions (gear shaped) icon at the bottom left and choose Select All, then press the Delete key on your keyboard.
For Calendars, open your calendar on icloud.com, click Edit on the bottom left, then tap the minus sign to the right of each calendar to delete it.
For Notes, open notes on icloud.com, click on each note on the left, then click Delete at the top to delete it.
For Reminders, open reminders on icloud.com, click on each reminder and press your Delete key to delete it.
For Mail, open your mail on icloud.com, click each folder on the left (such as your inbox), click on a single message to the right, press Control-A on your keyboard to select them all, then press your Delete key. Repeat this for each of your mail folders except Trash. When finished, click on the actions (gear-shaped) icon on the bottom left and select Empty Trash.
If you also want to delete your iCloud backups you can go to Settings>iCloud>Storage & Backup>Manage Storage on your device, tap the name of your device under Backups, then tap Delete Backup.
