Optimization is a part of bigger science called Operations Research (OR).
In a nutshell, operations research (O.R.) is the discipline of applying advanced mathematical and analytical methods to help make better decisions.

OR roots go back as far as 18th century when there was the first attempts to apply mathematics to plan UK mail operations.

Coming back to contemporary applications – birth of OR is attributed to WWII planning operations, such as for example when, where and how many troops and with what ammunition to position.

Optimization specifically helps you in situations when there are virtually innumerable number feasible options and comparing them is extremely difficult, optimization considers all available options and mathematically narrows them down to the very best ones.