A predecessor concept to aftertouch. A keyboard with second touch has a second set of switch contacts underneath the primary contacts. Pressing the key lightly engages the first contact, which (generally) causes the synth to which the key is attached to play a note. Pressing the key harder engages the second-touch contact. This might be used, for instance, to cause a pitch shift or bend, or to change the cutoff frequency of a filter. Unlike aftertouch, the second touch is an on-off function, and so not as useful. It is, however, easier and less expensive to implement.
Second-touch keyboards were pioneered by the theater organ manufacturer Wurlitzer in the early 20th century, which included the feature in many of its organ consoles. Few synths have used a second-touch keyboard; on that did was the EML Synkey.