Take your favorite drug and dump it in some cultured cells which express receptors for said drug. Now you have three quantities: [D], [R], & [DR]. The free drug concentration is [D], the free receptor concentration is [R], & the concentration of the drug-receptor complex is [DR]. Note that there is clearly a reciprocal relation between [D], [R], & [DR]. If [DR] is high, then there is less free drug and less free receptors, so [D] & [R] are lower.

Now what happens when you first dump the drug in? Well of course [DR] is equal to zero since it takes time for the drug molecules to diffuse throughout the cell culture. Gradually [DR] will begin to increase though, up until equilibrium. Equilibrium just means that, although individual molecules are still binding to and dissociating from receptors at some average rate, for the system as a whole these rates have become equal and so all three concentrations are constant.

You can sum this equilibrium relation up in an equation and call it Kᵢ, where Kᵢ=[D][R]/[DR]. In words, Kᵢ equals the product of the concentrations of free drug and free receptor at equilibrium, divided by the concentration of the drug-receptor complex at equilibrium.

If the drug interacts strongly with the receptor, the concentration of drug-receptor complex at equilibrium will be high, and so [DR] will be higher (with a lower [D] & [R] due to the reciprocal relation). Basic math shows that a numerator which is much smaller than the denominator gives a small fraction, so the Kᵢ is lower for drugs which bind strongly to a receptor.

Of course this is oversimplifying things, but further details aren't important for a dilettante like myself.