There are many different makes and models of tyres on the market, and knowing which type to fit to your bike's wheels can be a challenge. Here is an overview of what options are available.
Road bikes traditionally have narrow tyres with little or no tread (slicks). Tyres typically range between 23mm to 28mm in width, with more modern bikes often optimized for even wider tyres. Road bikes all have the same size wheels, 700c, which makes things a little simpler when choosing tyres. Rims however can differ slightly in width, so it's important to check this before choosing a wider tyre, in case your bike doesn't offer enough clearance. Most road bike rims are "clinchers" which means that tyres hook underneath a lip around the inside part of the rim whilst inflated. Some high-performance rims will be of the "tubular" variety, which means that only a tubular tyre can be fitted. Tubular tyres are often only used in racing circumstances due to their high cost and level of maintenance, though offer some performance advantages such as improved rolling resistance and less weight. Popular with mountain bikers, the "Tubeless" tyre is the most recent trend in road bike tyres, offering improved rolling resistance and weight savings, as well as improved puncture protection.
Hybrid/touring tyres are similar to road tyres in that they have less tread or are sometimes slick, and often the same size (700c) or 26". The main difference is that they are usually wider and heavier, offering greater puncture protection and longevity.
Electric Bikes come in all shapes and sizes, and many tyres are specifically designed to fit them. Ebikes are heavier and generate higher levels of torque. E-bike specific tyres have reinforced sidewalls to cater for this and will often be marked on the sides as such.
Gravel bikes are another more recent subgenre of bicycle, which often feature 700c or 650b size wheels. Gravel tyres need to be lightweight and fast-rolling, whilst also offering a decent amount of tread for offroad use. They are best used tubeless to prevent puncturing on rougher terrain, and to allow the tyres to be run at lower pressures, creating greater rolling resistance, better grip, improved comfort as well as puncture protection.
XC tyres are similar to gravel tyres in that they need to be lightweight and fast-rolling. They will typically be a little wider however, and fit 27.5" or 29" wheels (on modern adult size bikes.) If you are serious about choosing the best tyre, you will fit one that is suited to the time of year and riding conditions. If it's summer and you know it's going to be dry, a fast-rolling tyre with less tread is optimal, however, in winter or wet riding conditions, a softer tyre with more tread might be more suitable.
Trail/enduro/downhill MTB tyres are for offroad use and fit 26", 27.5" or 29" wheels. These are heavy-duty tyres with more tread than other tyre varieties. They will be wider, heavier and slower (on flat and uphill) but offer a great deal of grip and protection against rocks, roots and other obstacles which could tear a tyre open.