Standard deviation is a number corresponding to a bell curve describing how spread out the data is. Variance is a numerical value indicating how spread out the data is. Why are these two together? Because the standard deviation is the square root of the variance. Briefly, the math involved for computing these involves comparing each score with the average and then summing up the distance each score has from the average and comparing them to a standardized score, which has more math involved than we can compute. It's complicated, I know.
“Estimation statistics” is a fancy way of saying that you are estimating population values based on your sample data. Let’s think back to our sample ice cream data. First, let’s assume that we had a true random sample of 35 people on this globe and that our full target population is every human alive (7 billion people). Let’s say that 37% of people in our sample said that vanilla is their favorite flavor. Can we safely extrapolate that 37% of all people in the world also think that vanilla is the best? Is that the true value of the world? Well, we can’t say with 100% confidence, but–using inferential statistical techniques such as the “confidence interval”–I can provide a range of people that prefer vanilla with some level of confidence.