The OpenZeppelin project is built and maintained by a company called Zeppelin. The project is open source—anyone can use the Solidity contract files that are released by the project. The project contains many contract files that are mostly used by DApps to build upon and maintain the contract architecture. Many of the contract files that are present in the project have been battle-tested and are secure enough to be used in your project.
However, as a developer, you need to keep checking the issues that have been fixed on the OpenZeppelin GitHub project. You should always check the new OpenZeppelin releases and read the bugs list, which have been fixed in the new release. If a bug has been fixed in a contract file that you have used in your project, verify and ensure that your project contract code hasn't been affected; otherwise...