To manipulate something means to handle something skillfully. Like a sculptor manipulating clay or a really good politician working the crowd.
The verb manipulate evolved from manipulation, which back in the 1700s referred to a method of digging ore. So manipulating something originally only meant moving or arranging it by hand or mechanically. It wasn't until 1864 that people started using the word manipulate to describe someone exerting mental or emotional influence on others.