Some reactions are impossible or impractical to measure directly in a calorimeter — carbon burned in a limited oxygen supply won't stop cleanly at carbon monoxide, for instance, it keeps going to carbon dioxide. Hess's law is the tool chemists use to get the ΔH of such reactions anyway, by building them out of reactions that can be measured.
Enthalpy is a state function
Hess's law follows directly from a single fact: enthalpy depends only on a system's current state — its composition, temperature, and pressure — not on how it got there. That means the total ΔH for going from a set of reactants to a set of products is fixed, regardless of whether the reaction happens in one step or is built out of several intermediate steps. Add up the ΔH of any path between the same start and end points, and you get the same total every time.
Combining steps: reversing and scaling
To use the step-summation method, you find a set of reactions (usually ones with well-known, measured ΔH values) that can be added together — after some manipulation — to produce your target reaction. Two manipulations are allowed: reversing a step (running it backward), which flips the sign of its ΔH, and scaling a step by a coefficient (to match the stoichiometry of the target), which scales its ΔH by that same coefficient. Once the manipulated steps sum to the target reaction, their manipulated ΔH values sum to the target's ΔH.
The formation-enthalpy shortcut
Rather than hunting for a chain of measurable reactions every time, chemists have tabulated the standard enthalpy of formation (ΔHf) for thousands of compounds — the ΔH of forming one mole of that compound from its elements in their standard states. Because forming any reaction's reactants and products from elements is itself a valid Hess's law path, ΔH for the overall reaction is simply the sum of the products' ΔHf values (weighted by their coefficients) minus the same sum for the reactants. This is usually the faster method when formation data is available for every species involved.
Where this shows up in practice
Hess's law underlies how energy content is calculated for fuels, how reaction feasibility is estimated before running an experiment, and how textbooks derive the ΔH of reactions that would be dangerous or slow to measure directly (like partial combustion, or reactions of unstable intermediates). It's one of the first tools students meet for reasoning about thermochemistry without needing a calorimeter for every single reaction.