The early bicycles were called bone shakers because it rode on wooden wheels. Ouch! The addition of the bicycle tire made life more comfortable and safe. Tires fit snug inside the a wheel's hub and are typically large and hard to store but some models are folding for compact storage. The latest tire option is tubeless but this has not quite caught on in the recumbent trike and bike world.
Most recumbent trike riders are looking for a tire with excellent puncture resistance designed for touring and road conditions. The most popular size tires for trikes are 20" and 26". In the USA most trikes have two, 20" wheels in the front and a 26" wheel in the rear.
A tire is a circle so the width and height are the same. The tire dimension is written as radius by thickness. Tire dimensions have a long history and evolved over time. The actual radius of the tire is a "loose" measurement and is an approximation of the radius of the wheel's hub. The thickness of width of a tire is an even "looser" number: in other words, multiple tire width can fit onto the same bicycle hub.
When replacing a tire, look for ISO number on the tire (e.g., 40-406). This is the modern way tires are measured.