When we make a model or a map, the real (or actual) size of a feature cannot be depicted since it would take too much space (imagine having to make a full scale model of an airplane or a car). In order to save space, we make "scaled models". The idea is to have geometric similarity. This means that each feature is reduced by a certain specific factor. If the specific factor is 1, we call it a full scale model.
In general, we use a factor of more than 1. If we use a 1:10 scale, it would mean that every feature would be represented by a scaled down feature of exactly 1/10th size of original feature. Our entire model or map will be exactly 1/10 the size of our original feature.
In the given case, 1" = 1'. In other words, 1 inch = 1 foot (' is used for feet and " is used for inch). This would mean that any feature that has a size or dimension of 1 foot would be represented by a feature of dimension 1 inch. This is also known as a 1:12 scale (since 1 foot has 12 inches).
Hope this helps.