Both other and others have an indefinite meaning: other can be followed by a noun it modifies, whereas others cannot be followed by a noun. Their relationship can be described as: others = other + plural noun. Others is usually a pronoun
He never thinks of
others. (He never considers other people.)
I don’t like these books. Show me some others. (I don't like these books; show me some more.)
In the first sentence, others = other people, meaning “other people” or “others” in general, referring to everyone else; in the second, others = other books, meaning “other books”.
However, to express a definite meaning, we put the definite article before other and others. Likewise, other can be followed by a noun it modifies, while others cannot be followed by a noun, and the relationship still holds: the others = the other + plural noun. For example:
I started last in the race but I soon caught up with the others. (I was the last to start in the race, but I soon caught up with everyone else.)
Here the others = the other people, meaning “the other people”, where the definite article refers specifically to all the other people taking part in the race.
Note: besides a plural noun, the other can also be followed by a singular noun, in which case it cannot be replaced by the others. For example:
This seat is free; the other seat is taken. (This seat is empty; that one is occupied.)
Common idiomatic expressions
①one...the other means “one ... the other ... (of two)”. For example:
What I say goes in at one ear and out at the other. (What I tell him goes in one ear and out the other.)
②one...the others means “one ... the rest ... (of several)”. For example:
Of their five children, one is in China and the others are abroad. (They have five children; one is in China and the rest are abroad.)
Note: for three items, to say “one ... another ... the remaining one ...”, use one…another…the other [the third…]; for four, use one…another…another [a third]…the other [the fourth, the last].
③some...the others means “some ... the rest ...”. For example:
The search party was divided into two groups. Some went to the right, the others went to the left. (The search party split in two: some went right, the rest went left.)
④some…others means “some ... others ...”. For example:
Some people build while others destroy. (Some people build, while others destroy.)
Note: this structure can also be expressed as some…some. For example:
Some of us agree, some disagree. (Some of us agree, and some of us don't.)