What is SAP-BASIS?

SAP Basis is a set of programs and tools that act as an interface with Database, Operating system, Communication protocols and business applications (such as FICO, MM,etc).
Full form of BASIS is "Business Application Software Integrated solution".
SAP applications such as FICO, PP, MM etc. can run and communicate with each other across different Operating systems and Databases with the help of BASIS.

Basis supports a number of known operating systems (Unix flavors,Microsoft windows server edition,etc) and databases (Oracle, DB2, MaxDB, Microsoft SQL Server,etc)

How to check:

Login to system>navigate to 'system'>choose 'status'>select view application data on the screen> check fr SAP_BASIS component.
If it is there, means the system has NetWeaver Platform installed in it and the other applications like FICO, MM are running on top of it.
Also we can check for Support Package(SP) level, version installed in the system.