The average most people mean is the arithmetic mean: add the values and divide by how many there are. For 4, 8, 15, 16, 23 and 42 that is 108 ÷ 6 = 18. The calculator also gives the two other averages, because each answers a different question.
Median and mode. The median is the middle value once the list is sorted, or the midpoint of the middle two when the count is even, so 15.5 here. It ignores how extreme the ends are, which is why house prices and salaries are reported as medians: one very large value drags the mean but not the median. The mode is the value that occurs most often; a list can have several, or none, as here.
Spread. The range is the largest value minus the smallest. The standard deviation measures how far values typically sit from the mean. Use the population figure (divide by n) when the list is everything you care about, and the sample figure (divide by n − 1) when it is a sample from something larger; they match a spreadsheet's STDEV.P and STDEV.S.
Weighted average. When values count for different amounts, multiply each by its weight, add those up, and divide by the total weight. Marks of 85 and 92 that each count 30% and 78 that counts 40% average (2,550 + 2,760 + 3,120) ÷ 100 = 84.3, not the 85 a plain mean would give. The same arithmetic gives an average price from quantities bought, or a GPA from credit hours.