How or why "a Bitcoin address is a single-use token"? In the address wiki page it says that "a Bitcoin address is a single-use token". Do I have to understand one address is (or should be) used only once? 

More over, the Address reuse page seems to confirm that. But when reading some information here, this address 1F1tAaz5x1HUXrCNLbtMDqcw6o5GNn4xqX has 641 transactions. Could you please tell the points I misunderstand.
The bitcoin addresses are permanent addresses. You can re-use the addresses if you want. But when reusing it causes privacy issue as any one will be able to find out the number of transactions or the total balance that address has. (you found out that there are 641 transactions in that address).

To avoid this, its better not to reuse address and use separate address for each transactions, so that no one will be able to see your balance in the wallet or transactions.