In PHP (and lots of other languages), the logical operators use short circuit evaluation. That means, if the result of an expression is already determined after evaluating a part of the expression, then the rest won't be evaluated anymore.
In your example isset($var) returns false. Since the && operator is defined such that it is true only if all of its sub-expressions are true, this means that it cannot be true if the left sub-expression is false. Therefore, the right sub-expression won't be evaluated (and does not trigger an error).
Short circuit evaluation is very useful because you can combine a sub-expression that would lead to a runtime error with another one that guarantees that this doesn't happen. An example is the one that you have given. Other languages often use a similar construct for null-save constructs, e.g. if (foo != null && foo.bar == 1) in Java or C# - foo.bar would cause an exception if foo were null, but the virtues of short circuit evaluation guarantee that this will never be evaluated.