What is the advantage of using a T1 instead of analogue circuits, for example connecting two PBX's?
Using a T1 means that packet switching will occur so signals will travel the most efficient path through the network regardless of downed links. In circuit switching, a downed link means the signal will not reach it’s destination and a new connection would have to be made.

What does sub-multiplexing of a T1 mean?
Dividing the already multiplexed channels into even smaller channels.

What does subscribing to fractional T1 service mean?
If a subscriber doesn’t need all 24 channels of a T-1, they can get fractional T-1 service at a lower rate.

What are the advantages of using a T1 circuit instead of 24 analogue lines?
Total bandwidth of a T1 circuit is 1.544mbs. Advantages include the ability to use two twisted pair wires vs. 24 pairs, 24 connections for the price of 12 and is less subject to interference and static.

Twisted pair, bandwidth at 250 khz with speeds up to gigabytes per second.

Coaxial, bandwidth between 300-400 mhz, speeds up to 800 mbps.

Fiber optic, bandwidth at 2 ghz with speeds up to the terahertz per second.