If you're getting this error you're importing more fields than our limit, which is 700 fields. Unfortunately we cannot increase this number. However, you can still get your import to work without errors by setting enough fields to "Do not import". If you get the imported fields under 700 again, your import will run successfully.
You can set fields to "Do not import" in your import mapping. You can find your import mapping under "Setup > Edit mapping":
In the edit mapping you have to find the fields that you do not want to import and make sure the field is not a "custom" field. Next, choose "Do not import" from the drop down menu you see.