Often this is because some applications is "locking" the disk and refuses to let it go for an unmount.
Now how do we find out what application this is?

First step; determine where the disk is mounted - in Terminal.
Quite often this is a directory in /Volumes/, for example /Volumes/MyDisk.

Next step we use lsof  (list open files) in Terminal, but we do need sudo (admin) rights for that.

sudo lsof /Volumes/MyDisk

This should display a list, for example something like this:

COMMAND     PID USER   FD   TYPE DEVICE SIZE/OFF NODE NAME
mds         180 root   23r   DIR   53,2    16384    2 /Volumes/MyDisk
mds         180 root   27r   DIR   53,2    16384    2 /Volumes/MyDisk
Finder    11722 hans   51r   DIR   53,2    16384    2 /Volumes/MyDisk
QuickLook 11732 has    9r    REG   52,3  1143491 7862 /Volumes/MyDisk/SomePicture.JPG

Here we see that "mds" and "Finder" are currently accessing your disk.
In this care it's very unlikely that either of these "lock" your disk.

"QuickLook" on the other hand seem to have a file open - and is most likely the case the one locking your disk.

To stop this, you can "kill" that particular task as such - CAUTION when killing a task, unsaved data in the application will be lost!
First determine the PID, the Process ID. So here that would be "11732".
Next kill it:

sudo kill 11732