How do you know something to be true? One thing people have relied on for ages is seeing with their own eyes. When you see something happen, you know it to be true. It happened, in front of your eyes.
The easiest example of knowing if a transaction happened and was true, I often illustrate with an apple.
"When I hand over the apple, everybody can see that I just gave away the apple."
Imagine a group of people, I am the only one holding an apple. Everybody can see that I have an apple, while the rest does not. Everybody trusts their eyes that in the ‘apple ledger’, it would register that I have 1 apple, while the others would show an amount of 0 apples. Then a transaction is initiated. I talk to someone in the group. I tell this person I am handing him the apple. When I hand this person the apple, everybody in the group can see that I have just handed the apple to this other person. The ‘apple ledger’ should register my amount to be 0, this person should register 1 apple from now on. Everybody was a witness of this ‘transaction’ and everybody can agree, or reach consensus on this new ‘truth’ in the ‘apple ledger’ system.
For clarity, I am skipping a lot of technical details, and refer only to this as a high-level concept to understand the technology. Similarly, this is also happening in various blockchain technologies. The ledger amounts can be seen by all participants. The transactions can be seen to take place and all participants, or nodes, have to agree and reach consensus on the new state.