The idea
A correspondence is a traditional or symbolic association: rosemary with memory, the colour green with money, Monday with the moon. It links a thing you can hold to a quality you want to think about.
Not a physical claim
Correspondences are not statements about chemistry, biology or physics. A green candle does not contain money. Treating them as symbolic keeps the practice honest and keeps you out of trouble when someone starts making health claims about a plant.
Several systems, several origins
The lists in modern books come from different places: classical and medieval planetary magic, Renaissance and Golden Dawn ceremonial systems, European folk practice, the doctrine of signatures, twentieth-century Wiccan writing, and a great deal of twentieth-century invention. They disagree with each other constantly, which is a clue about their nature.
Your own associations count
A personal association, built from your own life, generally works better than one copied from a table. Your grandmother's lavender can matter to you without becoming ancient tradition. Just call it what it is.
Using them
Pick associations you can explain. If you can't say why a thing is on your altar, it is decoration, which is fine as long as you know that's what it is. Building a personal system properly is covered later in this path.