What is reason of having 3 phase in the transmission in cities?
It's the most efficient way to transmit AC

Let's say you are running 200A wires insulated for 5000 volts, for a nice round 1 MW capacity per wire one-way. 

If you run single-phase, you need 2 wires to complete the loop, and you get 1.0 MW circuit capacity. 

If you run 2-phase 90 degrees, you need 4 wires and get 2.0 MW circuit capacity.  

If you run 3-phase "delta", you need 3 wires and get 1.732 MW capacity. 

This is the most economical use of wire and terminations. 

It simplifies life for motors and DC loads

People who run motors love you, because 3-phase is the most efficient motor design, and it's fully able to self-start without burdensome compromises.  

You love people who are driving DC loads (i.e. rectifying 3-phase) because there's considerably less ripple between the most positive and most negative pole of 3-phase. This means things that ultimately use DC have much better Power Factors with less harmonics and inductive heating. (when you try to push a 300Hz harmonic through a 60Hz transformer). 

That drawing is wrong

The power on the top 3 wires is 3-phase delta.  There is no neutral here.  That wire labeled neutral is conspicuous in its absence of any insulators. It is a guy wire.  Note how the transformers are on the pole out of balance, their weight is pulling the pole over to the right.  Note also how the two down-guys are also pulling the pole over to the right.  Everything is teaming up to make this pole fall over, right?  No. 

The upper conductors are probably ACSR which means they have the dual role of also being in physical tension.  Those, and the lower cross-guy, are counter-balancing something that is happening on the pole to the left, off-picture. 

Given the bottom-tier insulators, I presume the lower lines are 480 "wye" service, with 480V corner-corner and 277V corner-neutral.  

"Why does neutral need insulation? It's near ground."  No, it's only near ground if everything is working properly.  The rest of the time, lookout!  That is why the lower service conductors do in fact have the same insulator on neutral as hot.