1. To oversee and monitor the process of growth, creation, or improvement of something
The project manager will supervise development of the new software application.
O gerente do projeto irá supervisar o desenvolvimento do novo aplicativo de software.
2. To direct and control the advancement or progress of a particular initiative
She was hired to supervise development of the company's marketing strategy.
Ela foi contratada para supervisar o desenvolvimento da estratégia de marketing da empresa.