Impress recruiters by knowing specific details about recent events affecting the company and the industry. Perhaps they recently hired new top executives or they were affected by industry, regulatory, or market changes.
Company profiles will often include a SWOT (strengths, weaknesses, opportunities, threats) analysis, strategy, competition, and recent acquisitions. You can find company profiles from Business Source Complete and Mergent Online. Databases like Bloomberg, Capital IQ, and Eikon will have financials, transactions, and peer analysis information.
If the company is publicly traded, it is essential that you visit their investor relations webpage and take a look at their most recent annual report and 10K or 10Q. Also check out recent press releases or presentations.
Finding a company's investor relations page is as easy as "Googling" the company name and "investor relations".