'Rollerball' can refer to pens with liquid or gel ink - we're specifically talking about liquid ink rollerballs here.
Unlike a ballpoint pen, which uses paste ink, a liquid ink rollerball doesn't require any pressure to get the ink to flow. As soon as the tip touches the paper, ink can flow. Pressing harder will normally give a broader line. The ball itself is smooth - coupled with the lack of pressure needed, this makes the whole writing experience smooth and easy.
Rollerballs are often seen as a cross between a fountain pen and a ballpoint - the smoothness and ink type of a fountain pen, with the convenience of a ballpoint.
If it all sounds a bit too perfect, there are a couple of small disadvantages. Rollerballs don't always work on shiny surfaces like birthday cards; and liquid ink can be relatively slow to dry, leading to the risk of smudging. This can be more of a problem for left-handed people, if your hand rubs over your writing.
The Uni-ball Vision Elite is a great all-round pen, with a good range of colours, and refillable in black, blue and red. Pilot V-System rollerball pens are hugely popular - including the iconic V5 needle-point roller. There are a huge number of high quality refillable luxury rollerballs from lots of manufacturers, and Lamy even have a couple of retractable rollerballs: the Tipo and the Swift. For a distinctly different writing feel, try OHTO ceramic-tip roller refills. As fitted to most OHTO rollerballs, the ceramic ball gives extra bite to the writing feel.