We consider if a solute is completely spread out through the solvent in the maximum possible extent, we consider the solute to be dissolved in the solvent. We can identify a solution by a few characteristics:
Solutions are uniform and have no precipitation or coagulated mass in it.
Solutions are clear, no granules or anything.
Solutions exhibit the phase of the solvent.
Solutions come under a more general category called mixtures. Mixtures can be either solutions, colloids, or suspensions. Lets see each one at the molecular level.
These have the solute finely dispersed as individual molecules throughout the solution.
These have the molecules in small aggregates and dispersed in a medium.
These have the molecules in very large granules. They are usually unstable and result in precipitation.
Now, coming to your question.
If a solute can disperse itself completely in a given solvent, its consider as soluble. In fact, every substance has some solubility in every solvent. Even benzene dissolves in water to a very very small extent. You may have heard of phrases like "soluble", "partially soluble" or "insoluble". Soluble salutes completely dissolve in the solvent, as well as amount of solute that can exist within the solvent is high. Acetone and Water are such an example. Some substances are what we would call as "partially soluble", they dissolve if a small but still perceptible amount of solute is added, but they do not dissolve if too much is added. Aniline would be described as "partially soluble" in water. Now, coming to insoluble ones, as I mentioned even they have a very little solubility, typically of the order of nanograms per liter. If you were trying to dissolve, say, benzene in water, you would probably take a few grams of benzene and mix. You won't be able to perceive the few nanograms that did dissolve in water, but the remaining large majority would be easily visible as undissolved. From the experimenter's point of view, he would consider it as insoluble since he can't really know that a few nanograms did dissolve. It's mostly based like this. However with more sophisticated equipment,you could measure the few nanograms, and then the they would say that benzene has a "solubility".
I hope I have clarified your doubts.