$$1 J = 1 N \cdot 1 m$$
Using dimensional analysis, we can see that this relationship is dimensionally consistent.
- The joule (J) is a unit of energy, which has dimensions of $[M][L]^2[T]^{-2}$.
- The newton (N) is a unit of force, which has dimensions of $[M][L][T]^{-2}$.
- The meter (m) is a unit of distance, which has dimensions of $[L]$.
So, when we multiply meters and newtons, we get joules:
$$[M][L][T]^{-2} \times [L] = [M][L]^2[T]^{-2}$$