A standard Hanukkah menorah, more precisely called a hanukkiah, has nine branches. Eight hold the lights representing the eight nights of Hanukkah, while the ninth holds the shamash, or helper candle.
The lights are added progressively: one on the first night, two on the second, and finally eight on the eighth night. The shamash is separate from that count and is used to light the other candles. It is commonly placed higher, lower, or to one side so it is visibly distinct.
The nine-branched hanukkiah is not the same object as the seven-branched menorah associated with the ancient Temple in Jerusalem. That seven-branched menorah is an important Jewish symbol, but it is not the candleholder used for the eight-night Hanukkah ritual. The phrase “Hanukkah menorah” is common in English, while “hanukkiah” is the more specific modern Hebrew term.