1. When the government raised the price of flour and sugar to the point where people could no longer afford them, the population was up in arms. Much of the population stopped work and gathered in the streets to protest.
2. The students were up in arms and began to protest against the school administration’s policies. They marched on the administration building, carried signs calling for the president’s resignation, and listened to speeches by the student leaders.

The expression is often used to describe groups of people rather than individuals. Arms refers to weapons. Thus the people are so angry that they are ready to take up weapons (at least figuratively).