Tip: See my list of the 
MostLearners of English quite often confuse the words “both” and “either”, probably because these tend to be translated using a single word into their mother tongue. The meaning of “both” is usually quite clear. It means “the one as well as the other”; for example, when you speak about two restaurants, you can say:
(The one restaurant, as well as the other restaurant, is good.)
A common construction is “both X and Y …” which means the same as “X and Y …”; only the fact that the statement is true for X and Y at the same time is emphasized:
(Peter, as well as his father, has red hair.)
The situation is slightly complicated for “either” because it is used in two similar but different situations. “Either” can be used in the construction “either X or Y” which means “X or Y but not both”. For example:
(I’d like to eat an apple or an orange but not both of them at the same time.)
is something you’d say when you want to eat just one piece of fruit. When “either” is not followed by “or”, the logic stays the same. It means “any one of two possibilities but not both of them simultaneously”. This is best illustrated by the most dangerous possible misunderstanding of the difference between “either” and “both”: when it comes to dosing medication.
Suppose you tell your doctor that you have two bottles of painkillers at home and you ask him or her which one of these you are supposed to take. If your doctor replies
it means you can take one or the other, but not both of them simultaneously unless the doctor further clarifies that you can. If he or she, on the other hand, says
the implied meaning is that it is safe to be taking the one and the other at the same time.
