What Does It Mean to Control for a Variable in Regression?

While interpreting the coefficient of one of the predictors (say a continuous variable X1) of an empirical model -- with multiple explanatory variables (X1, X2, …..Xn) predicting the value of an outcome variable (Y) -- you must have used these statements: "controlling for other factors/holding other factors constant/accounting for other factors/keeping other factors fixed, one unit increase in X1 is, on average, associated with b units increase in Y." But what exactly does it mean to control for a variable/hold a variable constant/account for a variable/keep a variable constant? In retrospect, I think the confusion originated because I thought regression is about fitting a straight line through some dots (which is correct but there are other ways of conceptualizing regression). In this article, using an intuitive toy example, I will try to answer these questions. I am intentionally using MS Excel for this article.