I recently learned that the word "either" has the meaning of "each of two" other than "one or the other of two people or things."
Two meanings seem to contradict each other, to me, and I wonder how people judge the word "each" mean.
For example, in the case of "the road was straight, with fields on either side," how do you know what the "either" mean?

See a translation

Good question! If the sentence is a question, or if alternatives are being presented, 'either' means 'one or the other of two'. We use 'either' to mean 'both' only in descriptions where no options are present; usually, this usage is only spacial.

You can grow a field on either side. (one or the other)
There are fields on either side. (both)
He's either tall or short. (one or the other)
There's a single palm tree at either end of the street. (both)
You can plant a palm tree at either end of the street. (one or the other)
She has a single diamond earring in either ear. (both)
You can get a single diamond earring in either ear. (one of the two)

Note that the following sentences are QUESTIONABLE or WRONG:
*Would you like to plant a field on either side of the road? (Using 'either' in a question involves some complexities.)
*He read Verne and Poe voraciously, and was a fan of either author.
*Either eye is blue. (Why? Because this isn't treating the body part as a location.)

I hope that helps!