Are you trying to import new entries or new categories (only)?
Assuming you are just importing categories…
As for the mapping step not showing, it sounds like an error is occuring during the processing that occurs after uploading the CSV file but before the mapping is displayed.
A lost of things may cause that to occur from a bad file to plugin / theme conflicts.
My first suggestion is to make sure the CSV being uploaded is a properly formatted CSV file.
Since this is a category import, the CSV file should contain only the following headers of which the last three are optional:
Name, Slug, Parent, Description
The exact names are not important since they can be mapped, but if you use the above names, they will be mapped automagically.
If you’ve already have done the above, the please try:
If that does not correct it, then move on to the conflict checks:
Hope this helps, let me know.