Actually, it called exposing to the right (refering to a histogram of your image.) . It can be overexposing in a way. You don't want to expose past the sensor limits, that is any luminance past the sensor limits is gone for good.
However, you do want to get the brightess values as close to the right edge as possible, without crossing the line. This could result in exposure, that is overexposed in the sense that it looks unnaturally bright. You would bring the exposure down to normal looking when you convert the RAW.
The reason for doing this is that you can get more detail in your shadow areas by recording them light and bringing them back down than by exposing them properly. While you can recover detail if you underexpose (to a point) the detail will be much lower quality and have a lot more noise.
A related issue, however is shutter speed. To expose to the right, you have to slow your shutter speed down, widen your aperture, or boost the ISO. Each of these options comes with issues that can affect your image, possibly in ways that take away the benefit of exposing to the right.
The technique is best for landscapes and stationary objects using a tripod, mirror lockup, and remote shutter to minimize the blurring from slowing the shutter speed down. Maybe portraits.
If you shoot handheld, candids, sports or other action, other considerations may be more important than exposing to the right.