The slippy map is the name used to mean the interactive sliding map viewer used on the front page of openstreetmap.org. It uses an open source JavaScript library called OpenLayers, and sets of map tiles that are assembled to form a continuous, movable image. Tiles for different zoom levels show different amounts of detail, depending on the rendering rules used. Apart from being the usual way of showing the map, it's also a tool for mappers to examine the data behind the map.
You can move the map around using the controls in the top left-hand corner of the map, and zoom in and out using the slider. You can also drag the map around with your mouse or pointing device, or zoom in and out using a mouse wheel, if you have one. You can zoom in on a particular area by holding down the Shift key and dragging a rectangle over the area you want to see. Double-clicking on the map will re-center the view and zoom in one level.
On the right-hand side of the map, you'll see a...