PHPUnit: expects method meaning

expects() - Sets how many times you expect a method to be called:

$mock = $this->getMock('nameOfTheClass', array('firstMethod','secondMethod','thirdMethod'));
$mock->expects($this->once())
     ->method('firstMethod')
     ->will($this->returnValue('value'));
$mock->expects($this->once())
     ->method('secondMethod')
     ->will($this->returnValue('value'));
$mock->expects($this->once())
     ->method('thirdMethod')
     ->will($this->returnValue('value'));

If you know, that method is called once use $this->once() in expects(), otherwise use $this->any()

see:
PHPUnit mock with multiple expects() calls

https://phpunit.de/manual/current/en/test-doubles.html#test-doubles.stubs

http://www.slideshare.net/mjlivelyjr/advanced-phpunit-testing

A look into the source code will tell you:

/**
 * Registers a new expectation in the mock object and returns the match
 * object which can be infused with further details.
 *
 * @param  PHPUnit_Framework_MockObject_Matcher_Invocation $matcher
 * @return PHPUnit_Framework_MockObject_Builder_InvocationMocker
 */
public function expects(PHPUnit_Framework_MockObject_Matcher_Invocation $matcher);

And the PHPUnit Manual lists the available Matchers at

• https://phpunit.de/manual/current/en/test-doubles.html#test-doubles.mock-objects.tables.matchers

• any() returns a matcher that matches when the method it is evaluated for is executed zero or more times.
• never() returns a matcher that matches when the method it is evaluated for is never executed.
• atLeastOnce() returns a matcher that matches when the method it is evaluated for is executed at least once.
• once() returns a matcher that matches when the method it is evaluated for is executed exactly once.
• exactly(int $count) returns a matcher that matches when the method it is evaluated for is executed exactly $count times.
• at(int $index) returns a matcher that matches when the method it is evaluated for is invoked at the given $index.