Infinity is a number larger than any finite number. A finite number is one that you can imagine; infinity is, therefore, unimaginable.
Many esoteric programmers seem to have a torturous relationship with infinity. It could be said that mathematicians embrace infinity, engineers aggrieve it, and programmers, being both mathematicians and engineers, are obliged to ignore it lest their heads explode.
To please strict constructionists who object that they just can't afford that much tape, these structures may also be described as unbounded - meaning that they are finite, but may grow when needed without limit. An analogy may be seen in lazy data structures, found in many programming languages.