PIV, or FIPS 201, is a US government standard. It enables RSA or ECC sign/encrypt operations using a private key stored on a smartcard (such as the YubiKey NEO), through common interfaces like PKCS#11.
You can read more about the PIV standards here: https://csrc.nist.gov/groups/SNS/piv/standards.html
PIV is primarily used for non-web applications. It has built-in support under Windows, and can be used on OS X and Linux via the OpenSC project.