The BitLicense is covered in full in the entry NY BitLicense, which explains who needs one, what the application involves and how the regime has been criticised. This page gives a short definition and explains the different names.
The BitLicense is a licence required by New York State for businesses that carry out virtual currency activities involving the state or its residents, such as transmitting, storing, exchanging or issuing digital assets. It is issued by the New York State Department of Financial Services under regulations finalised in 2015, and holders must meet requirements on capital, custody, cybersecurity, consumer protection and anti-money laundering. It was one of the first dedicated crypto licensing regimes in the world and is often compared with the US federal money services business registration and state money transmitter licences.
"BitLicense" is the informal name used by the industry and press; the formal term is a virtual currency licence under Part 200 of the state's financial services regulations. "NY BitLicense" simply adds the state to avoid confusion with other crypto licences. All three refer to the same licence.