Wolfram Mathworld gives us a more technical definition: The lemniscate, also called the lemniscate of Bernoulli, is a polar curve whose most common form is the locus of points the product of whose distances from two fixed points (called the foci) a distance 2a away is the constant a^2. This gives the Cartesian equation.
In other words, it looks like this on a graph:
Jakob Bernoulli published an article in Acta Eruditorum in 1694 in which he called this curve the lemniscus (Latin for "a pendant ribbon").
The lemniscate can also be generate as the envelope of circles centered on a rectangular hyperbola and passing through the center of the hyperbola (Wells 1991).
In other words, it would look like this on a graph:
