It looks like there are actually two titles here. Unfortunately, the common terminology for them makes things more confusing because the title 'Chair' can mean two different things.
First, many universities have endowed professorship positions within their various departments. In the United States, these positions are commonly called "Chairs" (or "Endowed Chairs.") These 'Chairs' are usually named after the person or group that endowed (permanently funded) the position. For example, my university department had a "Boeing-Stonecipher Chair of Computer Science," which was endowed by Boeing and its former CEO, Harry Stonecipher. The professor who currently occupies an endowed chair position is usually titled either as the name of the chair or as the name of the chair with the word 'Professor' replacing the word 'Chair.' To use the previous example from my university, the occupant of the position would be called the "Boeing-Stonecipher Professor of Computer Science" or the "Boeing-Stonecipher Chair of Computer Science." See this question from academia.se for more information on endowed chairs at universities.
Second, unfortunately, the "endowed chair" term can create some ambiguity because the head member of the faculty of an academic department is also usually called the "Department Chair." This title indicates the head administrative position within an academic department's faculty.
In the case of the citation given in the question, I would interpret "the Sidney J. Weinberg Professor & Chair of Computer Science" to mean that Dr. Silberschatz is both the Department Chair of the Computer Science Department and the current occupant of the Sidney J. Weinberg Chair of Computer Science at Yale.
However, I also must somewhat object to this professor's qualifications after seeing that he has written a book titled, Operating System Concepts with Java. :) Seriously, though, who uses Java to teach operating system concepts? That's what C and C++ (and sometimes assembly) are for.