"Ir" + verb ending with "ando"/"-iendo" means to do something progressively over time.
Sometimes you can use the verb "estar" instead, but with "ir" the idea of time going by is stronger, I think.
- El río se va/está secando poco a poco. -> The river is drying out.
- Es triste ver cómo el abuelo se ha ido/estado deteriorando con la enfermedad. -> It's sad to see grandfather wearing down because of his sickness.
- Iremos considerando todas las propuestas. -> We'll consider each and every proposal as we receive them.
- Mis joyas fueron desapareciendo con los años. Mis sobrinos se las robaron. -> My jewels slowly disappeared over the years. My nieces and nephews stole them from me.
In imperative form, it means to start doing something:
- Ve preparando la comida, que las visitas ya van a llegar. -> Start fixing food; the guests are almost here.
- Vayan lavando la ropa y mientras limpio la casa. -> Start doing the laundry and I'll clean the house in the meantime.
- Vaya abriendo la puerta, yo guardo el coche. -> Go open the door, I'll put the car in the garage.
And the best sentence in Spanish ever:
- Me voy a ir yendo. -> It must be something like "I'm getting ready to start to be leaving". It's a colloquial way to say we're leaving a place, like at the end of a party, to avoid abruptly saying "ya me voy".