Training is an activity which is done in order to increase the players' experience in one or more skills. Activities which are not done primarily for gaining experience are not usually considered to be training (for example, fighting the King Black Dragon in order to obtain rare item drops).
There are many ways to train skills. Some players prefer material gain during their training; others do not care so much, as long as they get their experience as fast as possible. Some skills are very commonly trained by buying the items required, such as Cooking, Prayer, Construction and Crafting. The items for these skills are therefore a common target for gold farmers.
The best way to train without becoming bored is to do something else at the same time. Activities such as reading, watching television, listening to music or even working out while training can keep focus up and boredom levels to a minimum.
In-game, it's good to switch training from one skill to another from time to time. Not only does it decrease monotony, but certain skills can be trained much faster and/or cheaper in conjunction with other skills. A good place to train is right outside of Lumbridge where you can chop trees, kill the local goblin population and visit the nearby fishing spot.