|| and && bind with the precedence that you expect from boolean operators in programming languages (&& is very strong, || is slightly less strong).
and and or have lower precedence.
For example, unlike ||, or has lower precedence than =:
> a = false || true
=> true
> a
=> true
> a = false or true
=> true
> a
=> false
Likewise, unlike &&, and also has lower precedence than =:
> a = true && false
=> false
> a
=> false
> a = true and false
=> false
> a
=> true
What's more, unlike && and ||, and and or bind with equal precedence.
Notice that because && is higher precedence than ||, the 2nd and 3rd clause are bound together, so there's no need to evaluate either of them once the 1st clause evaluates true:
> !puts(1) || !puts(2) && !puts(3)
1
=> true
But since or and and have equal precedence, the left-most and or or operator has higher precedence. In this case the or is left-most so it binds the 1st and 2nd clauses together. Because the second operator is an and, the 3rd clause must be evaluated to resolve the expression:
> !puts(1) or !puts(2) and !puts(3)
1
3
=> true
Observe that the parentheses force the and to bind the 2nd and 3rd clauses together, just as if it were an &&:
> !puts(1) or (!puts(2) and !puts(3))
1
=> true
The weakly-binding and and or may be useful for control-flow purposes: see Using "and" and "or" in Ruby.