ir vs irse
Ir is going toward a place. Irse is leaving, departing from where you are.
ir
To go to a destination — the focus is the place you're heading.
Voy al banco.
I'm going to the bank.
Destination. Always ir a + place.
¿Vas a venir?
Are you going to come?
Ir a + infinitive = going to do (near future).
Fuimos en tren.
We went by train.
Means of transport. Ir en tren/coche/avión.
irse
To leave, go away — the focus is departing from the current place.
Me voy, que llego tarde.
I'm off, I'm late.
Announcing departure. Not 'voy' alone, which would need a destination.
¡Vete!
Go away!
Reflexive imperative. Rude but common. Compare 'Ve' = go.
Se fue sin decir nada.
He left without saying anything.
Departure. Fue = he went; se fue = he left.
Tricky bit
'Fue al médico' (he went to the doctor's) vs 'se fue del médico' (he left the doctor's). Same movement, but ir is anchored to the destination and irse is anchored to the exit.