Import Contacts from CSV
Without seeing some of the actual file that is being imported, it is hard to say for sure. But my guess is that birth date field is an actual date field? And if so, it needs to be formatted as a date and on the first import screen you have to tell Civi how it is imported.

The error file that you can click and download will give you more information, as it will tell you what field(s) are the problem.