patient: slow to grow angry, holding heat back over time rather than flaring up
This is by far the most common and most important use of the word. It almost always appears in the phrase that the older English Bibles render "longsuffering" and newer ones render "slow to anger." The phrase is built on a vivid picture from the body: in Hebrew the same word means both "nose" and "anger," because anger was pictured as heat snorting out of flaring nostrils. To be patient, then, is literally to be "long of nostrils": the heat takes a long time to travel up and burst out. It describes a long fuse, not a cold heart.
The heart of this meaning is a single famous sentence. When God reveals his own character to Moses after the people worship the golden calf, he calls himself "merciful and gracious, slow to anger, and abounding in steadfast love" (Exodus 34:6). That self-description becomes the most-quoted statement about God in the Old Testament, and "slow to anger" is the one piece of it that every later writer keeps. Prophets and psalmists quote it back to God as grounds for hope and for forgiveness, and the same trait becomes a human virtue people are urged to imitate.
The word carries one important shade that English can blur: it is about time, not temperature. Being patient does not mean God or a person will never get angry; it means the anger is held off for a long while. That is why the very same phrase can ground hope in one place, where the long delay is still open, and dread in another, where the long delay is finally ending.