PokéBase - Pokémon Q&A
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31 IVs in a certain stat could potentially give you a difference of 31 stat points than a Pokemon that doesn't have those 31 IVs.

"For an example, let's say Greninja is a very popular competitive choice. It will be important for your Greninja to be faster than as many opposing Greninjas as possible because that's the difference between winning and losing against other Greninjas. 31 Speed IV (with +Spe nature) becomes a magic number. So, that 31 Speed IV becomes important.

Let's say both Greninja and Delphox are extremely popular choices. Let's say Greninja can 1HKO Delphox with Surf 100% of the time, but only if its SpA IV is higher than 20. Then, that 20 SpA IV is a magic number and is important. With 19 SpA IV, Greninja might fail only .83% of the time, but that will add up after all the Delphox you face. You really want a Greninja with 20 or more SpA IV.

Let's say Greninja can never 1HKO Delphx with Surf. It will always be a 2HKO at best. Then, it won't matter even if Greninja has 0 IV in SpA. If there are no other notable KOs that Greninja can do with more SpA IV (in other words, no benchmarks to meet), then it's a waste of time to get any SpA IVs."

As stated by MAtt5TER in this forum.

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IVs are important becuase they boost your Pokemons' stats so that they are more powerful.
Note: if this is ingame, it's not so important. But in competitive, this can mean the difference between a loss and a win.