Horizontal merger is a merger of two businesses operating in the same industry. It is a merger of competitors and is also called horizontal integration.
The basic motive behind horizontal merger is to gain from the economies of scale generated when a business operate at a higher production level. It also leads to increase in pricing power by gain in market share. Higher the market share of a business, greater the pricing power and greater the profitability. Horizontal mergers receive strict scrutiny by regulators (such as US Federal Trade Commission) before they are allowed.
If Dell and HP merge together, it will be a horizontal merger. It is because both Dell and HP are computer manufacturers and hence competitors so by definition the merger is a horizontal merger.