Maven is building tool/environment. Jenkins is a CI (continuous integration) tool.
Maven is more like a replacement for Ant.
It assists the building of the project through plugins e.g build and version control, JUnit tests, etc...
It manages dependencies of your project. you define how a project should be built(plugins), and what libraries are needed (dependencies) in a pom.xml file.
Jenkins as a smart job scheduler, can not assists you with tasks like version control or JUnit test, however, it can indirectly assists you with all this, by making calls to the pom.xml file in your project. And Jenkins gives you the power to decide when to call the pom.xml file, based on what condition to call, and what you want to do with the outcome. and Jenkins can listen to different events,