Why is this *unbounded limits*

 I don't think I can get the idea of the limit being unbounded, for instance, as shown above, lim h(x) seeing from the left side is called unbounded, but how is it possible for this line to go into infinity? Wouldn't it at some point reach a certain value and stop?    ( Does this make any sense? I am not quite sure how to explain what I am thinking...lol)