Think about some some of your favourite brands. Can you instantly identify a particular colour or colours that are practically iconic to each of them? Coca-Cola has red, National Geographic has yellow, Starbucks has green, McDonalds has red and yellow, Hermès has orange. If these brands were to use more colours, it would dilute that instant recognition.
By minimising the variation in their colour palettes, these brands gain ownership over a particular colour, ensuring a memorable and distinctive identity. If implemented well, your brand colour can remind your audience of your brand on its own, even when it isn't accompanied by your logo—such as Tiffany Blue, a colour that has been trademarked and is so well known that just the sight of a little blue box is an instant reminder of the brand.
As a general rule of thumb, a logo should not have more than one or two colours. Of course, there are exceptions to this (such as Google), but this rule is a good one to start with to ensure that your logo is not too overwhelming or amateur looking. A supplementary colour palette can be introduced to support the primary colours in the logo, but the proportions in which these colours are used should always be weighted towards one or two primary colours.
The choice of colours should also be based on an understanding of the brand itself—colour theory is a very important aspect of any branding project. Every colour has certain connotations and invokes a particular response, so this should be harnessed to enhance the message being conveyed by your brand. At the same time, a colour can have multiple meanings, for example, KFC uses red to convey energy and stimulate hunger, whereas British Airways uses red to convey a sense of warmth and comfort. This is why context is important, in terms of the industry in which your brand operates.
The right colour choice can help you attract the right audience and stand out from your competitors. Ensure your designer has researched the meaning of the proposed colours, including localisation—the same colour can mean very different things in different markets. In order to stand out, you also should not use the same primary colour as your close competitors.
Once the primary and secondary palettes have been defined, apply them across the board to all assets, whether digital, print, or even your office decor. Completely own the colour with no exceptions, and your audience will soon begin to associate it with your brand. Owning a memorable colour will set you apart in a world where people are overwhelmed by options!