PBX,Private Branch Exchange, as the name implies, its a small private telephone exchange, used in organizations for their internal telephone connections. Its also a basic telephone exchange, implemented in small scale unlike large telephone exchanges, but the basic technologies are going to be the same. Nowadays, almost all pbx’s are digital and so it is basically a digital switch, and so the human (analog)voice is converted in to digital using PCM (Pulse Code Modulation), and the pbx switches the pcm coded information from one time slot to other.
The digital switching two basic components Time Switch and Space Switch. Time Switch swiches the pcm coded voice between the time slot and space switch switches between the highway.For effective utilization in large and medium scale systems, these two components are combined in several combinations for better results. TST, TSST are the most popular configurations. The below links reveals some of the basics of the digital switching with block diagrams and circuits.
http://www.s-t.au.ac.th/~joey/Telephony7_2_2002_partone.doc
http://www.csse.monash.edu.au/~jwb/subjects/cse4891/spc/spc_sw.html
regds.