Continuous has its usual definition: a variable that "looks like the real numbers" in the sense that, for any value $x$ that the variable could take and any positive constant $\delta$, there's another value $y$ that the variable could take that's within distance $\delta$ of $x$. So, for example, the environment of your physician expert system will include things like the patient's temperature and blood pressure, which are both continuous, but it will also include discrete things such as what medicines they're currently taking and substances they're allergic to. There are also awkward cases such as how much pain they feel, which you might imagine to be continuous but is typically expressed on a discrete scale of 0 to 10. (I guess it's on a discrete scale partly because it's completely subjective and partly because nobody could distinguish between 3.298364 and 3.298365.)
However, note that your agent is most likely running on a digital computer. Because of this, any inputs it receives will have been rounded to some level of precision, making everything discrete in the end.