Said of a signal that increases or decreases at a constant rate, such that when it is viewed on a scope, the shape of the increase or decrease is a straight line. Also said of the response characteristic of something that accepts a control signal, such that when it is presented with a linearly increasing or decreasing signal, it reacts in a linear fashion. As an example, many envelope generators create linear segments; when viewed on a scope, the envelope generator's output consists of a series of connected straight lines. An example of linear response might be a common VCA, which for a given increase of X volts at the input produces an increase of Y volts at the output, where the ratio X/Y is constant for a given gain setting. See also exponential.
In integrated circuit marketing, "linear" is synonymous with analog, whether the device's output is actually linear or not.