DBMS means "Database Management System."A DBMS is a set of software programs that controls the system organization, storage, management, and retrieval of data in a database. DBMSs are categorized according to their data structures or types. The DBMS accepts requests for data from an application program and instructs the operating system to transfer the appropriate data. The queries and responses must be submitted and received according to a format that conforms to one or more applicable protocols. When a DBMS is used, information systems can be changed more easily as the organization's information requirements change.A DBMS allows different user application programs to concurrently access the same database. DBMSs may use a variety of database models, such as the relational model or object model, to conveniently describe and support applications.
Well known DBMSs include Oracle, IBM DB2, Microsoft SQL Server, PostgreSQL, MySQL and SQLite. A database is not generally portable across different DBMS, but different DBMSs can inter-operate to some degree by using standards like SQL and ODBC to support together a single application. A DBMS also needs to provide effective run-time execution to properly support (e.g., in terms of performance, availability, and security) as many end-users as needed.
Many DBA's think that RDBMS is a Client Server Database system but thats not the case with RDBMS. Yes you can say DBMS does not impose any constraints or security with regard to data manipulation it is user or the programmer responsibility to ensure the ACID PROPERTY of the database whereas the rdbms is more with this regard bcz rdbms define the integrity constraint for the purpose of holding ACID PROPERTY.