A parliamentary republic is a republic that operates under a parliamentary system of government where the executive branch (the government) derives its legitimacy from and is accountable to the legislature (the parliament). There are a number of variations of parliamentary republics. Most have a clear differentiation between the head of government and the head of state, with the head of government holding real power, much like constitutional monarchies. Some have combined the roles of head of state and head of government, much like presidential systems, but with a dependency upon parliamentary power.
For the first case mentioned above, the form of executive-branch arrangement is distinct from most other parliamentary and semi-presidential republics that separate the head of state (usually designated as the "president") from the head of government (usually designated as "prime minister", "premier" or "chancellor") and subject the latter to the confidence of parliament and a lenient tenure in office while the head of state lacks dependency and investing either office with the majority of executive power.
In contrast to republics operating under either the presidential system or the semi-presidential system, the head of state usually does not have executive powers as an executive president would, because many of those powers have been granted to a head of government (usually called a prime minister).
However, in a parliamentary republic with a head of state whose tenure is dependent on parliament, the head of government and head of state can form one office (as in Botswana, the Marshall Islands, Nauru, South Africa and Suriname), but the president is still selected in much the same way as the prime minister is in most Westminster systems. This usually means that they are the leader of the largest party or coalition of parties in parliament.