Why are biosignals from the body said to be continuous?
Biological signals are analogues and hence continuous. Early EEG systems simply recorded the analogue signals and displayed it as a continuous signal graphically as wiggly lines written by little pens on a roll of paper (Fig. 1). Only after analogue-to-digital converters became available, could EEG signals and the likes be digitally sampled. 


Fig. 1. Analogue EEG signal. source: Britton et al., 2016)  

Reference
- Britton et al., Electroencephalography (EEG): An Introductory Text and Atlas of Normal and Abnormal Findings in Adults, Children, and Infants, 2016. Chicago: American Epilepsy Society