We see a fair number of complaints about "duplicated" notes in Evernote's User Forums. If you have a large number of duplicates you may have network issues to look into (see below); but if there are only a few - take a close look to make sure that there are no content differences to take into account. It may be that more than one version of the note has been synced to the server and it is leaving it to you to sort out which is the correct one.
Background
Evernote keeps the 'reference' copy of all your notes on its cloud servers. Every time you view or edit a note online, your 'local' copy on the active device is checked against the server version. Any changes you make are saved back to the server so that other devices connected to the account can be updated ("synced") as necessary. It used to be the case, and probably still is, that any device on which Evernote is active will update from time to time.
Duplication of notes occurs when more than one version of an active note is presented to the server. The computer can't tell which is the latest version, so it saves both so its user can sort out which is the correct one. NB notes are saved as one item - i.e. it's not just the current changes; so each sync will take a little while - especially if this is a long note!
The server may see different versions of a note when
  • There's a bad network connection and the signal drops. In some circumstances the network will re-send the whole thing to make sure it's received.
  • More than one active device is syncing to the server - one may be routinely checking in with an older version of a note, the other being the one currently being edited.
  • The current device is being used over a long period and Evernote 'sleeps' or is temporarily put into background mode between changes by the device OS.
Avoiding the issue
The best way to avoid duplicates is to avoid long notes. If you're at a meeting, reading a book or watching a video and taking notes on that topic, make each thought a separate note. Save a common title prefix like "Gone with the Wind..." in a 'template' note and then save each thought with that title. Once you're done, merge the notes in created date (or any other) order, either then or later. Long notes are generally bad news. Apart from duplications, you can lose all your work with one fat finger move; at least with little notes you may only lose one thought...
Another way to avoid duplicates when you're editing a note may be to take your system offline deliberately and completely until you've finished the changes, then go back online to allow the server to be updated. If you need other network access during an edit, there are apps (I believe) which can block network connections for specific software: see Tripmode for example (h/t @PinkElephant). Block access / do your work / unblock again - and leave Evernote active so that it can sync the changes.
Failing any apps to help, it's actually better for long editing sessions (sorry Evernote) to use an external app which saves to your local device and copy/ paste the note contents into that, then back again in one operation when changes have been completed. Again leave the app active some time afterward to complete a sync.
If you're unable to fix the issue, then clearly advise Support - contact them via email / the feedback link in some apps, or their Twitter account - https://twitter.com/evernotehelps
The issue seems to be a 'feature' of how Evernote works at base level, which -obviously- is not going to change anytime soon. Being able to examine the activity logs of users where it is a problem may help the company at least reduce the number of instances.
If you've had the multiple copy issue and found other ways to avoid it, please let me know!