Fire is one of the four basic elements. It is commonly associated to energy, assertiveness and passion. Aside this, the element is present in most of religions, pre historic and now modern.
Fire also represents rebirth, after destruction. Phoenix for example is a bird of fire. This is the element that has place in every single myth and folklore, at how important it is.
Fire is also present in the Zodiac, as it's the element of Ares, Leo and Sagittarius. Which makes those signs positive and self-expressive, and especially fire also represents enthusiasm, drive to express self and faith.
Red is the color of blood, fire and rubies. Because of this it has always been associated with sacrifice, danger and courage, and later on with heat, activity, passion, sexuality, anger, love and joy; in China is the color of happiness. It's also associated with revolution, and it's the color of socialism and communism.
Again red is one of the first colors, along with black and white, used by artist during Upper Paleolith age, because with natural pigments it was one of the easier to make. In Eygipt red was associated with life, health and victory, and it's known that Egyptian women used red ochre as a cosmetic to redden cheeks and lips and also used henna to color their hair and paint their nails.
But red as a symbol is that of courage and sacrifice. When it comes to western countries it's mostly represent martyrs, that is because red is the color of blood. That is why the cardinals wear red coats, because that symbolizes the blood of Christ.
Mary, Queen of Scots, wore red shirt at her execution, as to show that she
was innocent martyr.
We can also say that red also is the symbol of romantic or country love and Valentine's day. Greeks and Hebrews considered red as symbol of love and sacrifice. But then it's also about happiness, celebration and ceremony. Think of the red carpet or what color are Santa Claus' clothes.
But red also is hatred, anger, aggression, passion, heat and war. You know when you are angry you say you "see red" and in Greek/Roman mythology red was the color of the god of war Ares/Mars.
Now days you will also know that red says danger and warning, think of the signs on the road, like: STOP. Or during soccer games, when a player gets a red card, and has to exit the game. Then for example red typhoon sign. It's the color that attracts attention, being noticeable.