Counterparty builds directly on top of the Bitcoin network, and every Counterparty transaction is a Bitcoin transaction as well. This means that Counterparty transactions are just as secure as Bitcoin transactions.
Because of this, Counterparty transactions must pay a small BTC fee to the Bitcoin miners for each transaction sent. Beyond being a sign of our commitment to the health of the Bitcoin network, this allows Counterparty transactions to be given a high priority and be confirmed quickly.
If speed of confirmation is not as important to you as the fee amount paid, note that it is possible to have lower fees in Counterparty, especially involving bulk sends. Ultimately Counterparty will support microtransactions.
If you're here because you've encountered the "Insufficient BTC at address ..." while trying to send BTC out of your wallet, please take a look at this page.
NOTE: there are Alternative Counterparty wallets that allow you to set your own (lower or higher) transaction fee. Most of them work with the same pass phrase that Counterwallet uses so no "migration" is necessary - they let you access the same addresses and accomplish Send operations faster or cheaper (because you can set the transaction fee or transaction priority to a higher or lower value).