Intuitive Explanation of R-squared Here is a nice definition of R-squared that I have found on the internet.


  R-squared is a statistical measure of how close the data are to the
  fitted regression line. It is also known as the coefficient of
  determination, or the coefficient of multiple determination for
  multiple regression.
  
  The definition of R-squared is fairly straight-forward; it is the
  percentage of the response variable variation that is explained by a
  linear model. Or:
  
  R-squared = Explained variation / Total variation
  
  R-squared is always between 0 and 100%:
  
  0% indicates that the model explains none of the variability of the
  response data around its mean. 100% indicates that the model explains
  all the variability of the response data around its mean. In general,
  the higher the R-squared, the better the model fits your data.
  However, there are important conditions for this guideline that I’ll
  talk about both in this post and my next post.


Could someone please explain to me what does "variability of the response data around its mean" stand for, and also "it is the percentage of the response variable variation that is explained by linear model"? I am having trouble understanding these concepts.
--variability of the response data around its mean---
It means the model You trained tells you how much Accuracy it can provide when predicting. Higher the R_squared ,More accurate the model.

it is the percentage of the response variable variation that is explained by linear 
This is literally the same question as above.