Good day I'll try to show you the differences by an example. Let's say that you are at home and there is a book "libro". - If the book is on a shelf while you are in the living room, then you might say " El libro está allí" meaning that it is there, can be seen but not close enough to pick it up. - If the book is on table next to you, then you say " El libro está ahí" meaning that it is there and it can be picked up. - If the book is far away, like on a table in the garden, then you say " El libro está allá". Hope this was useful.

As a Spanish teacher, I've always taught that "ahí" means there (nearby the speaker), "allí" means there (in the general vicinity of the speaker), and "allá" means there (farther away or, in relation to something that is "allí", beyond it). --¿Dónde está mi toalla? (Where's my towel?) --Está ahí, a tu lado. (It's there, at your side.) --No es mía... ah, allí está en la cama. (It's not mine...oh, there it is on the bed) --Sí, ésa es tuya, y la mía está allá en la ropera. (Yes, that one is your's, mine's over there on the dresser.) --