What is the purpose of the question marks before type declaration in PHP7 (?string or ?int)?

It's called a Nullable type, introduced in PHP 7.1.

You could pass a NULL value if there is a Nullable type (with ?) parameter, or a value of the same type.

Parameters :

function test(?string $parameter1, string $parameter2) {
        var_dump($parameter1, $parameter2);
}

test("foo","bar");
test(null,"foo");
test("foo",null); // Uncaught TypeError: Argument 2 passed to test() must be of the type string, null given,

Return type :

The return type of a function can also be a nullable type, and allows to return null or the specified type.

function error_func():int {
    return null ; // Uncaught TypeError: Return value must be of the type integer
}

function valid_func():?int {
    return null ; // OK
}

function valid_int_func():?int {
    return 2 ; // OK
}

Property type (as of PHP 7.4) :

The type of a property can be a nullable type.

class Foo
{
    private object $foo = null; // ERROR : cannot be null
    private ?object $bar = null; // OK : can be null (nullable type)
    private object $baz; // OK : uninitialized value
}

See also :

Nullable union types (as of PHP 8.0)

As of PHP 8, "?T notation is considered a shorthand for the common case of T|null"

class Foo
{
    private ?object $bar = null; // as of PHP 7.1+
    private object|null $baz = null; // as of PHP 8.0
}

References

As of PHP 7.1 :

Type declarations for parameters and return values can now be marked as nullable by prefixing the type name with a question mark. This signifies that as well as the specified type, NULL can be passed as an argument, or returned as a value, respectively.

As of PHP 7.4 : Class properties type declarations.

As of PHP 8.0 : Nullable Union Type

The question mark before the string in your function parameter denotes a nullable type. In your above example, $parameter1 must is allowed to have a NULL value, whereas $parameter2 is not; it must contain a valid string.

Parameters with a nullable type do not have a default value. If omitted the value does not default to null and will result in an error:

function f(?callable $p) { }
f(); // invalid; function f does not have a default