A perfect resource you might want to pick up to address this topic in more detail is Aarron Walter's Designing for Emotion.
All quotes below are taken from his book.
Every application has a personality. Define yours.
Personalities foster friendships and serve as the platform for emotional connections... Let's think of our designs not as a façade for interaction, but as people with whom our audience can have an inspired conversation. Products are people, too.
Using conversational language doesn't give your application a personality. It already has one. It may not be a great one, a well-developed one, or even a clear and concise one; but all applications have personality. Before you write copy, construct workflows, or design artwork, you should know what type of a personality your application should have. It should be a personality that they'll respond well to. That would communicate to them clearly and concisely. Is your personality buttoned-up or more casual? Define your application's profile and then create your language off of that profile.
If your website were a person, who would it be?
Applications should adapt.
Just as you adapt your conversation tone and vocabulary based on the situation, so also your application must adapt to the various circumstances users find themselves within. If you're introducing yourself, you can probably let language be a little more casual in nature (whatever casual means for your character). Yet if there's an error with a credit card transaction, continued use of casual language probably won't go over well. Instead of saying, "Hey buddy, there seems to be some issues...", let the user see that your application understands the severity of the issue by adapting it's conversation style. A better response would be, "I'm sorry, but there seems to be an issue processing your credit card. Could you verify your billing information? If everything looks correct, please contact us at ..."
Personality primes users for future situations.
You can't foresee the errors that will happen with your application, but they will come. Baking a intentional personality into your application, primes users to be more easily helped when those situations occur.
We can more easily help people troubleshoot problems when they are in a positive frame of mind, shortening the average support cycle [at MailChimp].
Emotion is the tie-breaking vote when too many options are equally valid. ... Remember, we don't have to make an exhaustive case for action because reason is not often the primary driving force our audience uses to decide.