“gift.” The Hebrew word is mattan (#04976 מַתָּן) and means a gift, offering, or present. In the context it is a gift given to curry favor, and that is the way it is used in Proverbs. It is used of gifts given for selfish reasons, including gaining an advantage over others. In this case, people with “gifts” gain entry to the rich and powerful, especially those in government whom they would otherwise not get to see, and that gives them a distinct advantage over the poor who cannot afford such gifts. It is in effect a bribe, but translating it “bribe” is going too far. A bribe is always considered wrong, while the gift here may or may not be immoral or illegal, even though it is given with the purpose of currying favor.
“creates opportunity.” The Hebrew word is literally, “enlarges,” or “makes wide” for him. Thus the gift enlarges his possibilities, it creates opportunity for him.
“leads.” The Hebrew word is nachah (#05148 נָחָה) and means “to lead,” or “to guide.” This is the figure of speech personification. The gift, or bribe, is now seen as a guide that leads the person forward on the path he desires to walk on but with which he is unfamiliar.