Median: the middle number in a set of data
(i.e. in the data set 11 12 13 14 15, 13 is the median. There are 5 pieces of data, so the 3rd piece is the middle because it has 2 pieces of data above and below it. In this case, the 3rd number is 13.)
Quartiles: Three values which divide the data set into four equal parts, with each part containing 25% of the data
(i.e. if our data is 1 1 3 3 5 5 7 7, our first quartile is said to be 2, because 2 data pieces are below it, our second quartile is 4 because there are two data pieces between it and quartile 1). this idea is also explained more in the video below.
Also...quartile 2 is the same as the median because it falls in the middle of the entire set
Once you have Q2, you can easily find Q1 by finding the middle number in the half of the data below the median, while Q3 is found by finding the middle number in the half of the data above the median
Box-and-Whisker plot: a graph used to easily display a set a data
This video explains how to find quartiles and draw a box and whisker plot. If you want a clearer drawing of the box, look below.
Some problems for you to try. I would for sure recommend trying example number two if you thought the examples given in the explanation were simple.