In hyperbolic space, lines can intersect or move away from each other, which is different from what happens in our usual flat space (called Euclidean space). This happens because in hyperbolic space, things curve outwards. Imagine drawing two lines that meet at a corner, and then continuing to draw them in a straight line. In hyperbolic space, the lines will move further apart and not meet again, while in Euclidean space, they will stay the same distance apart and never meet. This difference is caused by a special rule in hyperbolic space, which says that there are always at least two different straight lines that don't meet, no matter how far you draw them. This makes hyperbolic space look different from what we're used to!
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