Mergers and acquisition (M+A) is the name of departments of financial services firms whose job is to get companies to consider joining together or outright purchasing another company.
For a business, merger often means the end of the line: your business is integrating with another business that is similar in function and the cost savings/efficiencies of the joint company will be from eradicating the duplications of the companies. Firing, closing facilities and other cost-savings measures often follow.
Acquisitons are for two distinct purposes: to vertically own more of the business chain or to horizontally buy the competition. Vertical acquisitions mean that you are buying more of the chain of your business so that you can control costs or quality: you may be buying the distributor of your product, the manufacturer, the supplier, etc.. Horizontal acquisitions means that you are buying a direct competitor to either raise the price of goods or to potentially get products that you'd like to offer.