A trademark can be a logo, a jingle, a name or a combination of words and pictures describing your business. You would apply for it to be registered as a trademark by the IP protection agency in your country. If you would like to use the same trademark in other countries, you need to apply to authorities in the relevant countries. You could also apply with the World Intellectual Property Organisation.
For example…
Google owns a huge list of trademarks. Most of them have the name Google in it, in addition to other names that describe the product or service like Google AdWords or Google Dictionary. They however have others like Picasa or Chrome also registered as trademarks belonging to Google to describe their products.