Bower is a package manager for the web. It offers a generic, unopinionated solution to the problem of front-end package management, while exposing the package dependency model via an API that can be consumed by a more opinionated build stack. There are no system wide dependencies, no dependencies...
Yeoman is the scaffolding tool for creating modern webapps, which helps getting started and bootstrap your application with popular front-end tools and frameworks.
It is comprised of three tools: yo (the scaffolding tool), grunt (the build tool) and bower (for package management).