Bitcoin transactions are sent from and to electronic bitcoin wallets, and are digitally signed for security. Everyone on the network knows about a transaction, and the history of a transaction can be traced back to the point where the bitcoins were produced.
To send bitcoins, you need two things: a bitcoin address and a private key. A bitcoin address is generated randomly, and is simply a sequence of letters and numbers. The private key is another sequence of letters and numbers, but unlike your bitcoin address, this is kept secret.
Think of your bitcoin address as a safe deposit box with a glass front. Everyone knows what is in it, but only the private key can unlock it to take things out or put things in.
When Marie wants to send bitcoins to Peter, she uses her private key to sign a message with the input (the source transaction(s) of the coins), amount, and output (Peter’s address).
She then sends them from her bitcoin wallet out to the wider bitcoin network. From there, bitcoin miners verify the transaction, putting it into a transaction block and eventually solving it.