What does discrete mean in algebra?

In basic algebra a discrete variable is one that can only take on specific set of values.

For example, if we were to say that X can only take on a whole value between 1 and 10, then X would be a discrete variable.

On the other hand, a continuous variable is one that can take on an unlimited number of values.

For example, if we were to say X can take on ANY value between 1 and 10, then X is called a continious variable.

The important thing to note is that the range of a variable (the min and max values it can take) is different than whether it is discrete or continuous. Discrete only implies a fixed (and known) set of values is possible for a variable