Rust is a fungal organism that causes orange/brown growths to form on the grass. Rust will not harm the grass, but may turn your shoes brown.
A major Rust problem usually indicates that your lawn has poor grass (susceptible to disease) and might have poor soil quality.
Certain grass types are more susceptible to rust than others. Perennial Ryegrass is typically the most susceptible. You can improve your grass varieties by renovating or superseeding your lawn.
Diseases tend to be worse when the soil lacks microbial life. Improving your soil will help to reduce disease severity. The best way to begin improving your soil is to first really understand what you are working with. Soil Testing and balancing your soil, Core Aerating, Liquid Aerating, and Topdressing with Compost are a few ways to make a difference.