The number 24 can be shown as 2 tens and 4 ones, or as 20 + 4, or with 24 objects. Composing means putting tens and ones together to make a number; decomposing means breaking a number apart. This flexibility is essential for addition and subtraction algorithms.
You already know that numbers are built from tens and ones — that's what place value taught you. Now you're learning to move fluidly between a number and its parts. When you look at 47, you can see it two ways at once: as the single number "forty-seven," or as 4 tens and 7 ones (which is 40 + 7). Decomposing a number means breaking it into those parts. Composing means building the number back up from parts.
Think of it like a box of crayons. A box of 36 crayons is one thing — but inside, there are 3 full packs of ten and 6 loose ones. The number 36 and "3 tens, 6 ones" describe exactly the same thing, just in different ways. Being able to switch between those views is the skill you're building.
This flexibility becomes powerful when you add and subtract. Suppose you want to add 24 + 13. Instead of counting all the way from 24, you can think: "24 is 20 + 4. 13 is 10 + 3. So the tens together are 30, and the ones together are 7, which makes 37." You decomposed both numbers, added the pieces, and composed the answer — without any complicated steps. That's the payoff of knowing your tens and ones cold.