Pay Per Click (PPC) advertising focuses on those adverts you see at the top of Google (usually in a yellow box and marked 'sponsored links') that are paid for in order to get relevant traffic for certain search terms. Paid adverts like this are often the quickest way to get a top ranking and good results for competitive terms, while search engine optimisation focuses on the 'organic' search engine results and is a longer-term investment.
Brand bidding is the practice of focusing adverts on terms related to the brand of your company. It makes sense to bid on your own brand terms because you'll often find that certain people (customers and potential customers) will often prefer to click on Pay Per Click adverts over organic listings. Yes, it will cost you money to get them to your site, but if you get the bidding right it shouldn't cost much in cost per click terms and you'll see a good return on investment.
The other reason is you should never throw all your eggs in one basket. Relying exclusively on organic search is a risky practice which could lose you money if for some reason your website drops from the listings (e.g. you've employed a black hat company to handle your digital marketing) or you're just starting out and you don't appear in organic listings for your brand terms just yet.
The other reason to think about brand bidding is a competitive one. Google allows Pay Per Click advertisers to create adverts that bid on other company's terms (as long as trademark terms don't appear in the text of the advert) which means that when people search for your company name, a competitor might appear in the adverts and you could lose customers to the enemy. Tom Albrighton (@ABC_Copywriting) has written a nice article about PPC brand bidding which goes into more detail, but our focus here is on the importance of bidding on your own terms.
Will You Lose Customers?
There is question about whether brand bidding works. Obviously competitors bidding on your brands are trying to siphon off your customers to line their own pockets. The question of whether people searching specifically for your business, using your terms, could actually become a customer of a competitor is an interesting one.
Obviously if you have a loyal customer searching for you (rather than typing your URL directly into the browser) they are unlikely to be fooled by an advert from a competitor and even if they do click the advert, when they reach the competitors site they'll soon realise they are in the wrong place and click back to the search results, which means competitors have just cost themselves money for nothing.
However, searchers who have been recommended you by a friend might not realise they are in the wrong place and could buy from your competitor. Similarly, if your competitor is undercutting you in price of products/services they may get a conversion on that basis alone. So yes, there is some danger of losing potential customers to the competitors if you fail to bid on your own brand terms.
If you're unsure on the value of bidding on your own terms, do a quick search and see if a competitor already is. It's also important to consider how your customers use the search engines. Talk to friends, family and colleagues, get them to search for your brand terms and see how they use the results, you might be surprised.