Branding used to mean burning a mark on livestock with a hot iron to show who it belonged to. Then it became a symbol of luxury and created loyalty and followers. It became about selling values and beliefs as much as the product itself and now people are their brand. So things have changed quite a bit in recent years.
Your Brand identity is seen not only in your logo, but also the typeface, colours, photos and style of your website. You can have brand personality, sincerity and sophistication to tell your brand story etc so it can need quite a bit of thought and planning. Ultimately it is about trying to ensure website visitors and clients have a nice and memorable (for all the right reasons) experience when dealing with your business.