What is the advantages of the current value in battery?

For example, camera digital. If I use battery with 1700mAH and 2500 mAH what are the differences and the advantages?

2500maH has a larger capacity, meaning that it would last longer. For example, if the device drew a constant 170 ma (milliamps), a 1700 maH battery would last about 10 hours, whereas a 2500 maH battery would last almost 15 hours.

The 2500 mAH battery will last nearly 50% longer than the 1700 mAH. The figures relate to the storage capacity of the digital battery, the higher the number, the longer they'll last.
I've found Duracell batteries much superior to Energizer of the same capacity. The Energizer batteries lose their charge much quicker even lying around.

Batteries have the advantage over no batteries, as they have the power to power electrical appliances, making them portable, so that you dont have to plug it into the wall.

of course, the 2500 will last alot longer

A 2500mah battery will last longer. However they take a bit longer to charge. Last, make sure the device that your putting them into will support a 2500mah battery if it doesn't you could damage the components.