The simple explanation of the difference between là and ici is that là=there and ici=here. However, this falls short in several circumstances, where you'll always here one and never the other:

Viens ici! -- Come here. (that one's easy)
Je suis là. -- I'm here. That's the standard way of saying this.

My understanding is that là is a less precise description of a location than ici. Ici means "right here". Là is more general and can often also mean "here" in a more general and less precise sense.

Note that if you want to denote some other location, like "over there", you'd use là-bas.

Elle est là. -- She's here.
Elle est là-bas. -- She's over there.

Thank you so much for the explanation and the examples, Chris!