What is covariate? I'm confused with this term: covariate.  What is it? Is is just the observed outcomes of some random variables that contain information that could help us enhance our prediction of another random variable that we haven't observed yet?  Why is it named so?
Also there seems to be another:  independent variable.  Independent of what?  Why is it named so?
 A: From Wikipedia:

Depending on the context, an independent variable is sometimes called a "predictor variable", regressor, covariate, "controlled variable", "manipulated variable", "explanatory variable", exposure variable (see reliability theory), "risk factor" (see medical statistics), "feature" (in machine learning and pattern recognition) or "input variable." In econometrics, the term "control variable" is usually used instead of "covariate".

Answering (some of) your questions:


*

*Assume that you are solving linear regression, where you are trying to find a relation $\textbf{y} = f(\textbf{X})$. In this case, $\textbf{X}$ are independent variables and $\textbf{y}$ is the dependent variable.

*Typically, $\textbf{X}$ consists of multiple variables which may have some relations between them, i.e. they "co-vary" -- hence the term "covariate".


Let's take a concrete example. Suppose you wish to predict the price of a house in a neighborhood, $\textbf{y}$ using the following "co-variates", $\textbf{X}$:


*

*Width, $x_1$

*Breadth, $x_2$ 

*Number of floors, $x_3$

*Area of the house, $x_4$

*Distance to downtown, $x_5$

*Distance to hospital, $x_6$
For a linear regression problem, $\textbf{y} = f(\textbf{X})$ the price of the house is dependent on all co-variates, i.e. $\textbf{y}$ is dependent on $\textbf{X}$. Do any of the co-variates depend on the price of the house? In other words, is $\textbf{X}$ dependent on $\textbf{y}$? The answer is NO. Hence, $\textbf{X}$ is the independent variable and $\textbf{y}$ is the dependent variable. This encapsulates a cause and effect relationship. If the independent variable changes, its effect is seen on the dependent variable. 
Now, are all the co-variates independent of each other? The answer is NO! A better answer is, well it depends! 
The area of the house ($x_4$) is dependent on the width ($x_1$), breadth ($x_2$) and the number of floors ($x_3$), whereas, distances to downtown ($x_5$) and hospital ($x_6$) are independent of the area of the house ($x_4$). 
Hope that helps!
A: the way linear regression is generally run (there are ways to ask for different slope calculations) you are getting the unique impact of one predictor on the dependent variable. Its shared impact with other predictors on the DV (or indirect impact as with structural equation models I believe) is not part of the slope. it is sometimes stated that the slope is the impact of a specific predictor setting all other X to zero (although that breaks down obviously when some X can not take on the value of 0 or you have interaction). 
A: 
In general terms, covariates are characteristics of the participants
  in an experiment. If you collect data on characteristics before you
  run an experiment, you could use that data to see how your treatment
  affects different groups or populations. Or, you could use that data
  to control for the influence of any covariate.
Covariates may affect the outcome in a study. For example, you are
  running an experiment to see how corn plants tolerate drought. Level
  of drought is the actual “treatment,” but it isn’t the only factor
  that affects how plants perform: size is a known factor that affects
  tolerance levels so that you would run plant size as a covariate.
Another example (from Penn State): Let’s say you are comparing the
  salaries of men and women to see who earns more. One factor that you
  need to control for is that people tend to earn more the longer they
  are out of college. Years out of college, in this case, is a
  covariate.
A covariate can be an independent variable (i.e., of direct interest)
  or it can be an unwanted, confounding variable. Adding a covariate to
  a model can increase the accuracy of your results.

Source: https://www.statisticshowto.datasciencecentral.com/covariate/
