A theoretical construction which is very useful in simplifying physical theory. An isolated system is a set of objects which are free to interact with each other but do not (for whatever reason) interact with any other objects. One does not define the system by a volume, since then objects could leave or enter. Rather, one selects the relevant objects.
But what's the big deal? It closes off what you need to consider. You don't need to worry about anything else. Looking at the whole system is achievable when you have a finite system. Thus, isolated systems are an idealization used in Reductionism.
Also, one gets a more concrete gain: conservation laws only apply to isolated systems. Since no actual systems other than the entire universe are completely isolated, this may seem useless. However, it is quite common that a system will be close enough to isolated for government work.
For example, a tossed tennis ball, besides being pulled by gravity, is buffeted by air molecules and light and neutrinos. Unless there is high wind (or a nearby supernova), it behaves like the theoretically isolated tennis ball of a high school physics problem. Note that the isolated system must include the Earth, since that is what provides the gravitational force acting on the tennis ball.
Sometimes a system is isolated for some purposes but not others. Hot coffee you are carrying in a thermos is pretty close to isolated from your hand, for the purposes of thermodynamics. Mechanically, however, it is not.
It is also possible to consider isolated systems in non-physical law such as sociologically isolated people.
In any case, an 'isolated system' is an approximation made to delimit a law in a theory. Experimentally, devices or situations can be engineered which bring a system close to isolation, to great utility. However, natural systems are not usually so simple.