There are two common reasons for the error: Unable to Create Directory /abc/def/xyz: Is its parent directory writable by the server?
1) This is the obvious one, and many people try this first and it may not help. You need to make sure your uploads folder located by default in wp-content/uploads and all folders/files below it are writable by the server. The easiest way to do this is to change the permissions to 777 recursively.
2) If #1 didn’t work, then your issue is most likely this: Go to your WordPress Admin Interface -> Settings -> Media and look at the value for the “Store uploads in this folder” setting. It should be “wp-content/uploads” by default but sometimes I’ve seen mine change on a whim to attempt a full server path and ends up breaking. Change it back to the default and it will probably work fine.
If it’s still not working, comment below and we’ll see if we can figure it out.