Before Bitcoin, to use digital money, we needed a trusted third-party to keep a ledger of who owned how much. Examples of this trusted third-party are MasterCard, VISA, your bank or your MNO if you use mobile money. So if Alice sent Bob £100, this trusted third-party would debit Alice's account and credit Bob's account - they would update their ledger and we all had to trust this 'trusted' third-party to do the right thing and be good stewards of our money.
Now with Bitcoin, everyone has a copy of this ledger so we mo longer need to trust a single entity/organisation/third-party because there is no need to trust when you can just verify against this ledger because you have a copy of it. This decentralised ledger is called the Blockchain BTW.
And the other thing is that everyone using is following the same rules we are so we don't even need to trust them because we know that Bitcoin was built to make it impossible to break the rules.