My other half's a primary school teacher so have picked up a bit about number bonds by osmosis (she works every evening and most weekends).
They're first and most commonly taught to 10 and 20, e.g. number bonds to 10 are 1-9, 2-8, 3-7, etc. As kids go through years 1 and 2, they're expected to learn various different number bonds for the numbers up to 20 (and beyond), like those in the questions posted by the OP.
They help us split numbers in useful ways (ways that make sums easier and help embed principles) or put another way, how numbers join together, which introduces the concepts of addition and subtraction. They also help with the idea of inverse calculations, and that addition is the inverse of subtraction.
Don't think I've explained that the best and can see why some have said they seem pointless, but knowing a few instant, simple facts like the difference between 10 and 6 will always be 4, etc can help people have functional maths skills.