A business decides it needs software when something stops scaling: a register that no longer fits, a spreadsheet that three people edit at once, a report that takes a full day to assemble. The instinct is to look for a product. The better first move is to draw the process.
Mapping means writing down every step from trigger to outcome, naming who performs it, and marking where information is created, checked or lost. It is unglamorous and it usually takes an afternoon. What it produces is a shared picture that survives disagreement, because everyone can point at the same drawing.
Two things fall out of the exercise almost every time. First, some steps exist only because a previous system demanded them, and can be deleted rather than automated. Second, the real bottleneck is rarely where people assumed it was — it tends to sit at a handover between two departments, not inside either one.
Only then does a software decision make sense. You now know which steps must be supported, which can be dropped, and what a system has to prove before you sign. If a vendor cannot demonstrate the bottleneck step in a demo, the demo has not told you anything.
This is also why we start engagements with discovery rather than a proposal. A quote written before the process is understood is a guess with a number attached.