degrees of freedom
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Think of a person on a dance floor. They can step forward and back, left and right, and spin around — those are the separate ways they can move. Count them up and you have counted that dancer's degrees of freedom: the independent kinds of motion or change available.
In physics, a degree of freedom is one independent way a system can move, point, or store energy. A single atom flying through a gas has three: it can move along three directions in space. A molecule made of several atoms has more, because it can also rotate and its atoms can vibrate against one another. The total number of degrees of freedom tells you how many separate things you would need to specify to describe the system fully at one instant.
This matters because counting degrees of freedom is how physicists predict how matter stores heat: each active degree of freedom can hold a share of thermal energy, which sets a material's heat capacity. A common subtlety is that some degrees of freedom can be frozen out — at low temperatures certain vibrations or rotations simply do not switch on, because quantum mechanics forbids them from taking small amounts of energy.
A robot arm with three joints has three degrees of freedom — three angles you can set independently. To say exactly where the hand ends up, you must give all three; that count is what lets the engineer reason about every pose the arm can reach.
Three joints, three degrees of freedom: three numbers fix the arm's pose.
Degrees of freedom are not the same as the number of atoms: one atom in three-dimensional space already has three, and large molecules can have dozens once rotations and vibrations are counted.