Strictly speaking a secure credit card does not build credit history. As the term suggests, you are required to provide security against the usage of the credit card. For example, if you want a credit card that has a limit of $1000, then you will first need to deposit this money in an account that is linked to the credit card. If you failed to make the payment on your credit card bill then the lender can simply withdraw the money from the security deposit in order to cover the bill.
You must however always make sure that this does not happen as the intention of getting a secure credit card is to display to the lender that you can handle credit responsibly and can be trusted with being provided with a regular credit card.
The reason why a secure credit card does not build a credit history directly is that the majority of them are not reported to the credit bureaus. For this reason any transaction that you make on the credit card will not be reported and will have no effect whatsoever on your credit score.
However, this could be the road to take in the scenario where all other efforts of building a credit history has failed. By using a prepaid credit card judiciously and displaying money management, you can convince the lender to upgrade your secure credit card to a regular credit card. If it is your own bank that has issued a secure credit card then you will find it all the more easier to migrate to a regular credit card. Once you get a regular credit card you can building your credit history.