I'm not sure you posted this in the right place, you might have gotten a response (or more responses) sooner if it was posted in, say, CCNA R&S or something else that was related to routing and switching. Anyhow, I will try to answer your question as best I can.
The extended system ID is utilized by spanning-tree to include the vlan ID in the STP bridge ID, it also uses the same MAC address in each bridge ID. So, normally the bridge-priority would be a value from 0 to 65535, with a default of 32768. With the extended ID, the value will be the vlan ID plus the bridge priority value, with a range of 0 to 61440 for the bridge priority value, in increments of 4096. Note, the bridge priority value will never be higher than 61440 as the last increment of 4096 in the use of the extended system ID, because with a bridge priority value of 61440 plus the vlan value of 1024 it still remains under 65535, which is the highpoint of the priority value. If you were able to use the last value 65535, any vlan ID added to that value would exceed the limits set for the STP bridge priority value (the 16-bits allocated for that portion of the 64-bit bridge ID).
Bitwise, a normal STP bridge ID contains a 16-bit bridge priority (0 to 65535) , followed by a 48-bit unique MAC address for the VLAN. With the STP extended ID you have a 4-bit priority multiplier (0 to 61440) followed by a 12-bit vlan ID, followed by a non-unique (common) MAC address. The use of a non-unique MAC address is also called MAC address reduction. In the non-extended system ID for STP, the switch would assign a unique MAC address (the switch has a certain number reserved) to each instance of STP (one per vlan). With the extended system ID, this is not the case, as the same MAC is used for all instances of STP.
Also, on switches that do not support 1024 unique MAC addresses for its own use, like the 2950, the extended system ID is enabled by default.
Del provide you a very nice explanation. Good job Del. Check out this link
to a calculator I created in MSExcel that shows you how the bridge ID and VLAN ID make up the bridge priority value. Please let me know if you have any questions. Sheet 1 is the "extended system ID" and Sheet 2 is the "traditional system ID".