The simple answer is that it makes protractor not wait for Angular promises, such as those from $http or $timeout to resolve, which you might want to do if you're testing behaviour during $http or $timeout (e.g., a loading message), or testing non-Angular sites or pages, such as a separate login page.

For example, to test a button that sets a loading message during a request you can set it to true when fetching an element + checking its contents

element(by.css('button[type=submit]')).click();

browser.ignoreSynchronization = true;

expect(element(by.css('.message')).getText().toBe('Loading...');    

browser.ignoreSynchronization = false;

expect(element(by.css('.message')).getText().toBe('Loaded'); 

A more involved answer is that setting it to true means that subsequent additions/injections to the control flow don't also add browser.waitForAngular. There are cases when an understanding of the control flow, and when/how things are added/injected into it is important. For example if you're using browser.wait to test a multi-stage process, the function passed to wait is injected into to the control flow after the rest of the functions in the test have added to the control flow.

element(by.css('button[type=submit]')).click();

browser.ignoreSynchronization = true;

expect(element(by.css('.message')).getText().toBe('Stage 1');

browser.wait(function () {

   // This function is added to the control flow after the final

   // browser.ignoreSynchronization = false in the test

   // so we need to set it again here 

   browser.ignoreSynchronization = true;

   return element(by.cssContainingText('.message', 'Stage 2')).isPresent().then(function(isPresent) { 

     // Cleanup so later tests have the default value of false

     browser.ignoreSynchronization = false;

     return !isPresent;

   });

});

expect(element(by.css('.message')).getText().toBe('Stage 2');

browser.ignoreSynchronization = false;

expect(element(by.css('.message')).getText().toBe('Stage 3');

An alternative to using browser.ignoreSynchronization is to access the standard webdriver API directly

element(by.css('button[type=submit]')).click();

expect(browser.driver.findElement(by.css('.message')).getText().toBe('Loading...');    

expect(element(by.css('.message')).getText().toBe('Loaded'); 

Using the driver methods directly to find the elements means that the system will try to find them without waiting for any ongoing $http requests to finish, much like setting browser.ignoreSynchronization = true.