In a metric space you have a way to measure distance and thus the definition of boundedness is, in a sense, obvious. In a topological vector space there are no distances, so of course the definition will be different than that given for metric spaces simply since you can't state the metric definition without a metric. However, if you think about it, the intuition is still the same. Try contemplating the definition. Stare at it for a while, translate it back to a familiar (metric!) topological vector space until you realize that it says essentially the same thing only using a more general language, since that is all you have.