A Digital Mirrorless Camera is a Digital Camera that accepts different lenses but does not have a mirror and mirror box to switch the scenes inside the camera from the optical viewfinder to the imaging sensor and shutter. Instead, most viewfinder functions are electronic. This allows the camera body to be smaller, thinner and lighter. These are also known as MILC cameras - Mirrorless Interchangeable-Lens Camera.
In many cases, these smaller bodied cameras also fall into the category of 4:3rd cameras (Four/Thirds Cameras) or Micro 4/3 cameras. This refers to the shape and dimensions of the actual image sensor (4:3 instead of the traditional 3:2 layout) and allows for many different camera systems to use each other's lenses.
If you need something with good image quality but need a more portable camera for travel purpose, you would be best off getting a Mirrorless Digital Camera. These cameras offer similar high image quality as the SLR Cameras - as the sensor is often similar in size - but do not contain mirror and prism systems and are thus more compact and lighter. Mirrorless Cameras still have an interchangeable lens system so you can have the benefits of a range of specially designed, high quality optics.