Say you wanted to guess someone's weight, but you only know their height. How could you do this?
If you had access to measurements of the the height and weight of many people you could draw up a graph with height and weight on the axes and put dots at the points of each pair of measurements. What you will see is a general trend for taller people to be heavier, but there is a lot of scatter around this trend.
Regression is the process of using some technique to estimate the typical relationship between the height and weight. So, after doing the regression analysis you might be able to say
Typically, someone who is 1.8 metres tall weights about 80Kg, but someone 2
metres tall weighs around 100Kg.
Of course plenty of people who are 1.8 metres tall weigh more or less than 80Kg, but your analysis might tell you that in the absence of any other information your best guess for their weight is 80Kg. The regression analysis tells you how this typical value for weight changes with height i.e. taller people are typically heavier.
Regression is not limited to one variable predicting another, for instance what if we also knew the biological sex of each person? After doing some regression analysis we might be able to say
Males that are 1.8 metres tall typically weigh around 85Kg but Females
weigh around 75Kg.
Note that I just made up all these numbers. The actually numbers would depend on doing some regression analysis on a real data set (which I haven't done for this quick explanation).