Other, The Other, and Another

with count nouns :

an + other + singular noun (one more)

• another pencil -> one more pencil

the + other + singular nouns (last of the set)

• the other pencil -> the last pencil present

other + plural noun (more of the set)

• other pencil -> some more pencil

the other + plural noun (the rest of the set)

• the other pencil -> all remaining pencil

with non count nouns :

other + noun . count nouns (more of the set)

• other water -> some more water

the other + noun . count nouns (all the rest)

• the other water -> the remaining water