Purpose of cylindrical attachments on Power Transmission towers

I'm assuming you mean these two:

The official name for these is "Distribution transformer".

They are the "local transformers", here's a schematic of how they could be connected:

Which is from this question

Actual connections and voltages depend on the country so details may be different.

The large cylindrical devices as indicated below are power line transformers. Their function is to step down the higher distribution AC voltage down to the common mains line voltages that feed into residences and businesses.

The larger DT is 3 phase voltage stepdown, while the smaller one uses only 1 phase for local use residential use.