JavaBeans and Servlet are both concepts part of the Java EE (Java Enterprise Edition) package release in 1999/2000.
The servlet is a Java class (used as an Controller) in a java Web Application. Its role is to manage the HTTP Request and generate an HTTP Response. The Servlet is using JavaBeans to get its information from the database for instance.
The JavaBean is a simple java class used to represent the model of your application. To be called a JavaBean, the class must have public getters and setters for all its properties, must have a no-argument constructor, and must be serializable.
It is interesting to understand that this simple JavaBean concept migrates to the Enterprise Java Bean (EJB) in early 2000. But experience proved that EJBs were quite complicated to managed in the Java EE environment. Consequently, Enterprise JavaBeans were mostly replaced by "Pojos" (Plain Old Java Object) popularized by IOC Containers (like Spring in 2003). IOC pulled back Javabean to its former concept. IOC replaced the overall EJB-J2EE Templating pattern, Service Locator, Business Delegate patterns to a simple Injection of Dependencies (DI).