Please help with understanding of specification text

[Forp]

https://en.bitcoin.it/wiki/Script reads:

The script for a typical Bitcoin transfer to destination Bitcoin address D simply encumbers future spending of the bitcoins with two things: the spender must provide a public key that, when hashed, yields destination address D embedded in the script, and a signature to show evidence of the private key corresponding to the public key just provided.

and I am unfortunately too stupid to understand this.

The spender wants to transfer money to destinatin address D. This destination address is the hash of the public key of the account to which the money is transfered. Right ?

But how can the spender produce a signature to show evidence of the private key? The spender does not have the private key to the "public key just provided", since this is the place he sends the money to.

So, obviously my understanding is wrong here.

Where is my mistake ?

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[joan]

The spender wants to transfer money to destinatin address D.

Here.
The spender controls address D and wants to transfer money to someone else.

Alice send money to Bob on his address D.
To spend them again, Bob will have to 1. Have the public key corresponding to the address D, 2. have the private key corresponding to the public key.
The script is evaluated to see if someone has the right to redeem received coins.

[theymos]

The sender encumbers the coins with restrictions. The person who spends those coins meets the specified restrictions.