To understand tonicity, imagine the following scenario: you have a tank of water that has a selectively permeable (i.e. semi-permeable) membrane, which, for the purposes of this example, allows water (not solute) to flow freely. If you fill one side of the tank with some kind of dissolvable solute - in this case, let's say table salt - the water with the freshly added solute will now have a greater tonicity than the other side of the tank. In other words, the side of the tank that contains the table salt has more solute than the other, and therefore is considered "hypertonic" relative to the side of the tank that just contains water and no solute.
The concept of tonicity is rooted in comparing the solute concentrations of solutions, which are often separated by a semi-permeable membrane and allows for the free movement of water. A common physiological example is that of a cell (as described above), which has a cell membrane that allows for water to move inside or outside of the cell depending on the intracellular and extracellular concentrations of solutes. The following terms compare how "tonic" one solution is compared to another:
Hypertonic: one side of the semi-permeable membrane has a higher concentration of solute than the other
Hypotonic: one side of the semi-permeable membrane has a lower concentration of solute than the other
Isotonic: both sides of the semi-permeable membrane have an equal concentration to each other
In our example above, the side of the tank that has table salt is considered to be "hypertonic" to the other side that only contains water. Moreover, the side that only contains water is considered to be "hypotonic" to the side that contains the table salt.
Now, what happens in this example since water is able to move freely between the membrane? Water always flows from a high concentration of solute to a low concentration, so it will move to the side that contains the table salt to dilute the concentration relative to the side with no table salt, generally until both solutions on either side of the membrane are isotonic (i.e. equal in concentration) to each other.
With all this in mind, how does tonicity impact cells in the body? If a cell is "hypertonic" relative to the extracellular environment, since the cell membrane is permeable to water (but generally not solute, at least in this case) water will begin to move into the cell and the cell will swell. Conversely, if a cell is "hypotonic" relative to the extracellular environment, or the extracellular environment is "hypertonic" compared to the intracellular environment, water will move out of the cell and into the extracellular space - the cell will shrivel. If the cell is isotonic compared to its extracellular environment, all is well and there is no water movement observed.
These concepts are very important when it comes to considering how dehydration effects the cells in your body - for example, dehydration affects multiple organ systems as the lack of water in your blood increases the "drive" for water to exit the cells and enter the bloodstream - this is, water moves from the intracellular environment to the extracellular environment, as the cells shrivel, which can have negative consequences on organ function.
I hope this helps!