'Rollerball' can refer to pens with liquid or gel ink, normally dispensed by a smooth ball.
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.
Gel-ink rollerballs have a fairly similar feel to liquid-ink rollerballs, but do normally require a little pressure to get the ink flowing. They tend to give a more consistent line width, dry a little quicker, and can hold pigment, or even particles for metallic or sparkling effects.