Minimum and Maximum Values cover range of values attached to any spawn or recruitment template. They indicate the minimum and maximum numbers of troops a vassal may recruit or the size of an army/unique spawn/warband/patrol upon spawning.
The range on this allows some variation, meaning that if an army spawns once, it'll have x troops, but if another same army spawns just after, it'll have similar numbers.
The actual numbers are only influenced by player's level, the rest is randomness. This means that player will see everything spawn with smaller numbers in the early game, and as he progresses and becomes stronger, so will the AI.
However, numbers are still randomized, player level affects the minimum value, from a scale going from X to Y, where 0 is the minimum value, X the player level, Y is player level*4+15 and 100 the maximum value. A random number will be chosen for each and this will determine the amount of that troop the spawn will appear with/the lord will recruit.
Example: from the Obrist Heynrich picture, 200-300 Mettenheim Spieszknechts.
If the player is level 1, Obrist will spawn with a random number between 201 and 219. If the player is level 30, he will spawn with a random number of these troops between 230 and 300.
Another example, using his Mettenheim Greatswords. 50 is his 0 value, 90 will occur when the 100 is randomly chosen. If the player is level 1, the range of values is 1-19, meaning that if he gets a 10, he will get 54 Greatswords (minimum value + difference between min and max * number chosen as a %) using the formula (50 + 40*10%) we get 54. If the player is level 30, the number will range between 30 and 100. If he gets a 50 for the Greatswords, he will get 70 Greatswords (middle value).
This means the max will reach 100 when he hits level 21.5 (as 21.5*4+14=100).
Player's level is checked for these spawns every 42 hours, meaning that if the player raises several levels, it'll take over a day for it to be noticed.