A trademark is a distinctive, non functional characteristic of a product, service or brand, that the brand owner claims as property and importantly, defends against misuse by others.
A trademark can be pretty much anything sufficiently distinctive; for example chocolate maker Cadbury has trademarked the purple colour they use in packaging, and Nike has trademarked their "tick" logo.
A trademark is easier to defend if you have registered it. Trademark registration generally only applies within one jurisdiction so you may need to register a trademark over in every country where you think it has value.
You must actively use a trademark, meaning that you must trade in the jurisdiction and use the trademark when you do. If you don't actively use the trademark you run the risk of a court denying you the right to defend it if someone else uses it.
If you own a trademark in a jurisdiction, you can use it yourself in marketing your product, and you can license it to someone else to use on your behalf. If anyone uses it without your licence, you can tell them to stop and ultimately, get a court order telling them to stop (and perhaps pay you costs and damages).
It is not uncommon for a business to claim a trademark that is already in use by someone else- for example when it is the surname of the founder. This can be tricky- even if the business succeeds in registering the trademark, courts may not allow them to enforce it against someone who already uses it for their own business.
A trademark is an asset of your business. For many businesses, intangible assets such as trademarks, patents and registered designs are extremely valuable. However, it can be difficult to ascribe a monetary value to them, so some businesses do not include them in their balance sheets, which under-values the business (affecting credit rating as well as share value). The monetary value of a trademark is proportional to the advantage it gives you over competitors. There are rules of thumb to value a trademark but any single estimate produced that way is subject to challenge.