Compare a database connection to a cash register in a super market. If there is only one, everybody has to line up at that one single cash register to pay for their shopping. Imagine how long this line could become if there are several dozens of people wanting to pay.
So just like there often are multiple cash registers to help multiple people at once (thereby splitting the single long line into multiple shorter ones), multiple database connections allow more requests to be handled at once. In any web application this is really a must, otherwise your website could only service one user at a time.