What are the uses of clocking and timing ports on Juniper routers There are 4 ports each named "Ext Ref clock", "TOD", "1PPS", "10Mhz" on MX104. I understand what each stands for and have vague idea of each after googling but what are they used for in real world?

Their main use is for providing extremely precision timing for services such as Synchronous Ethernet or SATOP - essentially carrying TDM services (such as an E1 or T1) over Ethernet.

This is quite common in Telco, but also in industrial control systems too (rail comes to mind), where they need to interface with a lot of legacy TDM circuits and deliver them using modern networking equipment.

You attach a GPS antenna, or other precision time source directly onto the MX via those SMA jacks, enable SyncE and then downstream devices are synchronised over directly attached Ethernet interfaces.