What is this operator <=> in MySQL?

It is the NULL-safe equal to operator

<=> Operator is used to compare NULL values with the fields. If normal =(equals) Operators return NULL if one of the comparison value is NULL. With <=> operator returns true or false. <=> Operator is same as IS NULL.

From the manual:-

<=> performs an equality comparison like the = operator, but returns 1 rather than NULL if both operands are NULL, and 0 rather than NULL if one operand is NULL.

mysql> SELECT 1 <=> 1, NULL <=> NULL, 1 <=> NULL;
        -> 1, 1, 0
mysql> SELECT 1 = 1, NULL = NULL, 1 = NULL;
        -> 1, NULL, NULL

Edit:-(Although very late to add one important side note mentioning NOT <=> as well)

On a side note:-

NOT <=>

There is one more point NOT <=> which is used to compare NULL values with the fields. If normal != or <> (not equals) Operators return NULL if one of the comparison value is NULL. With NOT applied to <=> operator returns true or false. NOT applied to <=> Operator is same as IS NOT NULL.

Example:-

SELECT NULL != NULL,         //--Result is NULL
   NOT NULL <=> NULL,        //--Result is 0
   NULL IS NOT NULL;         //--Result is 0

is <=> NULL-safe equal to operator

This operator performs an equality comparison like the = operator, but returns 1 rather than NULL if both operands are NULL, and 0 rather than NULL if one operand is NULL.

See here for the documentation

Sample :

you should use IS NOT NULL. (The comparison operators = and <> both give UNKNOWN with NULL on either side of the expression.)

SELECT * 
FROM table 
WHERE YourColumn IS NOT NULL;

can also negate the null safe equality operator but this is not standard SQL.

SELECT *
FROM table 
WHERE NOT (YourColumn <=> NULL);

TL;DR

It's the NULL safe equal operator.

Like the regular = operator, two values are compared and the result is either 0 (not equal) or 1 (equal); in other words: 'a' <=> 'b' yields 0 and 'a' <=> 'a' yields 1.

Unlike the regular = operator, values of NULL don't have a special meaning and so it never yields NULL as a possible outcome; so: 'a' <=> NULL yields 0 and NULL <=> NULL yields 1.

Usefulness

This can come in useful when both operands may contain NULL and you need a consistent comparison result between two columns.

Another use-case is with prepared statements, for example:

... WHERE col_a <=> ? ...

Here, the placeholder can be either a scalar value or NULL without having to change anything about the query.

Related operators

Besides <=> there are also two other operators that can be used to compare against NULL, namely IS NULL and IS NOT NULL; they're part of the ANSI standard and therefore supported on other databases, unlike <=>, which is MySQL-specific.

You can think of them as specialisations of MySQL's <=>:

'a' IS NULL     ==> 'a' <=> NULL
'a' IS NOT NULL ==> NOT('a' <=> NULL)

Based on this, your particular query (fragment) can be converted to the more portable:

WHERE p.name IS NULL

Support

The SQL:2003 standard introduced a predicate for this, which works exactly like MySQL's <=> operator, in the following form:

IS [NOT] DISTINCT FROM 

The following is universally supported, but is relative complex:

CASE WHEN (a = b) or (a IS NULL AND b IS NULL)
     THEN 1
     ELSE 0
END = 1