Dependent and independent variable refers to what you are keeping constant in order to observe a change, think cause and effect. An independent variable is one that is used to observe the change. This could be time, the concentration of substance, etc. A dependent variable changes with variation of the independent variable. looking at them together, you can observe how the independent variable affects the dependent variable.
For example, how time (independent variable) affects reaction progression by observing product concentration (dependent variable). Time is not changed by the presence or absence of the product, thus it is independent. However, time will dictate how much product is formed as the chemical reaction progresses, thus, it is dependent on time.
Another common example is how concentration (independent variable) affects the absorbance of light (dependent variable). Based on the relative concentration of a substance in a sample, the absorbance will increase or decrease. Because absorbance is dictated by concentration, absorbance is dependent. Concentration is not changed based on the absorbance, so it is independent.
Graphically, the independent variable is on the x-axis (horizontal) and the dependent variable is on the y-axis (vertical). In a graph header/title, the typical format will be (dependent vs. independent). For example, (product concentration vs. time) and (absorbance vs. concentration).