Of all the characteristics of a bike's tyre, grip is the most important, as it defines the ability of the tyre to brake hard without the wheel locking, of accelerating without loss of grip and of negotiating bends and changes in direction without skidding. In other words, it is synonymous with safety.
Rubber is, of course, the main component, but there are also many other compounds or chemical elements, such as silica, for example. The exact composition of tyres is an industrial secret which is closely guarded by manufacturers.
One usually talks about "soft rubber" and "hard rubber" to distinguish the grip of different tyres. A soft tyre gives intrinsically more grip than a hard tyre.
Each tyre, and thus each chemical composition, has a corresponding range of optimal operating temperatures. Each tyre has maximum grip at a given temperature or range of temperatures. Grip increases with the tyre's temperature until maximum grip is reached. Grip then decreases (often at the same time as the tyre itself deteriorates) if the temperature continues to rise.
The temperature of a tyre increases depending on the mechanical stress to which it is subject: driving, accelerating, braking and taking bends are all actions which cause the tyre's temperature to increase. As a rule, soft tyres have an operating temperature which is higher than a hard rubber tyre and take longer to increase in temperature.
Besides the specific grip achieved by each model of tyre at a given temperature, one must also bear in mind that grip also depends on the surface of contact with the ground and the state of the surface being driven on. The greater the surface of contact between the tyre and the surface, the greater the grip. If one takes equally wide tyres, a tyre without tread or with little tread thus gives better grip than a tyre with a lot of tread. This, however, is only true on a dry surface.
In fact, on a wet surface, a large tyre with little tread runs a greater risk of aquaplaning. The phenomena of aquaplaning is caused by loss of the tyre's grip on the road. A surface of contact which is reduced to zero is equivalent to grip which is reduced to zero. The role of tread is to evacuate water and to stop a wave from forming at the front of the tyre - the cause of the phenomena of aquaplaning.
Each type of tyre has a speciality. One must therefore define the use and conditions of use of one's bike in order to choose the right tyre.
For example: a "sport" tyre will not necessarily be the tyre which gives the best grip if the bike is mainly used for short urban trips in a cold and wet climate. Even though, in theory, the "sport" tyre gives maximum grip which is far greater than a road tyre, it will never have the opportunity to achieve maximum grip because it will never be able to reach its optimal operating temperature during short urban trips.
On a wet surface, a "sport" tyre will run the risk of aquaplaning due to its relative lack of tread. For this type of use, a "road" tyre would be more suitable. As its operating temperature is relatively low and quickly reached, it will operate in its optimal temperature range and will thus give greater grip than a "cold" sport tyre. Moreover, on a wet surface, it will reduce the risks of aquaplaning due to the size of its tread.