How do ordinals work?

Could you please explain how ordinals operate? I'm really curious about how they function within the realm of mathematics and language. Do they have specific rules or patterns that govern their usage? Also, how do ordinals differ from other numerical expressions? It seems to me that they play a unique role in conveying order and sequence. Could you elaborate on this, perhaps with some examples to illustrate the point? I'm eager to learn more about this fascinating topic.