Web sites are unfortunately prone to security risks. And so are any networks to which web servers are connected. Setting aside risks created by employee use or misuse of network resources, your web server and the site it hosts present your most serious sources of security risk.
Web servers by design open a window between your network and the world. The care taken with server maintenance, web application updates and your web site coding will define the size of that window, limit the kind of information that can pass through it and thus establish the degree of web security you will have.
"Web security" is relative and has two components, one internal and one public. Your relative security is high if you have few network resources of financial value, your company and site aren't controversial in any way, your network is set up with tight permissions,
your web server is patched up to date with all settings done correctly, your applications on the web server are all patched and updated, and your web site code is done to high standards.
Your web security is relatively lower if your company has financial assets like credit card or identity information, if your web site content is controversial, your servers, applications and site code are complex or old and are maintained by an underfunded or outsourced IT department. All IT departments are budget challenged and tight staffing often creates deferred maintenance issues that play into the hands of any who want to challenge your web security.