Horizontal and vertical analysis of financial statements deal strictly with the time period in question for analyzing the statements. Horizontal analysis takes a look at a specific aspect of the business throughout different time periods for comparison. For example, a horizontal comparison will look at a single factor, like overhead, cost of goods sold, or sales throughout different time periods. If you are comparing overhead from each quarter of the year or comparing overhead for quarter 3 of 2017 to Quarter 3 of 2016, then you are performing a horizontal analysis. This gives an understanding of how certain elements of the financial worksheet have changed over time.
A vertical analysis looks at the comprehensive view of the financial worksheet for a specific time period. You would analyze all of the different factors—profit, cost of goods sold, overhead, sales, etc, for a single quarter or year. This gives a comprehensive viewpoint of the company's finances as a whole for that time period. A vertical analysis would tell you how much money the company has earned and spent in a certain time period.
Both of these elements are useful for analyzing a company's performance. While either factor individually can be good or bad, a healthy company will have positives for each of them, to show that profit has improved over time and is currently positive.