The post I have quoted below is well worth a read, (and part of a series on the importance of employee engagement) 

As someone who interacts with a whole range of companies, I think it's not only vital for internal reasons, but also external. 

Working with them - It's more fun to work with people that are engaged in what they do,  meeting them is fun, they are more productive, easier to work with and you never have to deal with that negativity and listlessness that haunts some companies.

Working for them - when you meet someone who is engaged and interested in their job, you can often imagine how much fun it might be to work with them. If you are a candidate looking for a job and you meet a happy and engaged team, you are much more likely to says yes if the job is offered.  

Buying from them - who would you rather buy from? The happy engaged salesperson or the angry desperate and disinterested one.

Engaged employees become advocates for your company, they sell your products, attract your new recruits, delight your customers and create interactions that potential clients remember when they finally get to the point of needing your services....