The Apache PhoenixQueryServer (PQS) is a relatively new (early 2015) component that has been added. Previously, users of Phoenix had at least two things in common: the client was written in Java and the Phoenix client libraries were included in that client. As Phoenix continues to grow as a dominant player in the "Hadoop OLTP" space, the need to eliminate these two burdens became apparent. PQS was the solution chosen to address these problems.
PQS specifically refers to an HTTP server which can interact with a custom JDBC driver that translates JDBC API calls to HTTP requests. These components are provided by an upstream Apache project, Apache Calcite, specifically the Calcite component referred to as Avatica. Originally, the HTTP requests were JSON; however recent work (mid-2015) has also shown that serialization using Protocol Buffers is also feasible.
The excitement behind PQS is two-fold as alluded. Java-based clients now have two means of running queries: a typical JDBC client with all of the necessary dependencies and computation local (the phoenix-client jar taking 10's of megabytes in space) or using the new "thin" client which offloads the majority of computation to PQS and a very small deployment footprint (little more than an HTTP client). The bigger excitement is the RPC API implicitly exposed by PQS. With a stable RPC API, this allows clients in any language to implement their own thin-client to PQS, enabling "native" access to Phoenix.
It is important to realize that PQS is still very much a work in progress effort. While efforts are ongoing to ensure that PQS is a fully-featured, secure, well-performing, and stable system. There has not been enough effort to guarantee any of these to date (2015, likely into 2016); however, there are visible strides being made in these areas.