In some job markets (afaik Silicon Valley, and most high-prestige medical or legal positions) you can get multiple offers within a few days of each other, and this matters for driving up compensation, particularly the signing bonus when present.

edit for clarification: This works by keeping all interested companies/firms/hospitals in the loop on where you are in the interview process with the other prospective employers. If they don't ask, you, the prospective employee, volunteer this information. Prospective employers adjust their interview schedules accordingly. Sometimes, volunteering information that you're in demand and about to leave the job market because you have an offer in hand is enough information to get an offer when another prospective employer would otherwise would just keep looking, hoping somebody better might become available in the next couple weeks.

Probably by asking to match the offer in hand.