https://bulbapedia.bulbagarden.net/wiki/Effort_values
That would pretty much answer all of your woes regarding EVs. I highly recommend reading that. I highly, highly, HIGHLY recommend you read about all of this and completely understand in order to appreciate the whole aspect of EVs.
Macho Brace halves your pokemon's speed (literally halves it) in exchange, any pokemon you defeat will give double the EVs gained. The Macho brace DOES NOT add any attack or defense to your pokemon. It helps them grow stronger through the doubled amount of EVs they gain.
Basically, each pokemon hides certain effort values based on a certain stat. For example, a Poochyena when defeated gives 1 EV on attack. Getting effort values will help your pokemon become stronger on that certain stat. It doesn't matter what level of that pokemon is. A lvl1 Poochyena and a lvl100 Poochyena will give out the same amount of EVs when defeated.
Essentially, the Macho Brace will help you max out the stats that you HAVE TO MAX OUT in a
shorter amount of time.
The more important answer for you would be? Why should you care? Well even for the non-competitive battling aspect (or in better words, NOT PVP) knowing EVs is great for your pokemon for a couple of things:
1) You get to max out the stats that your pokemon should max out, making your pokemon excel on what they are made to do. For example: Blaziken is a strong and speedy Physical Attacker with low defense. So I EV Train Blaziken on Attack and Speed by collecting the said ATK and SPEED EVs. Now, with that, should i have properly EV Trained Blaziken (since its days as a Torchic and Combusken), it should end up with really high amounts of ATTACK and SPEED to help him sweep down other pokemon without worry.
2) Battle Tower (R/S) or Battle Frontier (E) - This is pretty much the end-game aspect of Pokemon RSE. Basically this is where you put the rest of your pokeskills to the test, and Battle Tower/Frontier is pretty much known for letting the player battle things in the game beyond the difficulty of the Elite Four and Champion. Basically put, if you do not have properly EV Trained pokemon when you go to these areas, you'll either get wrecked really hard or worse. You need to have well trained Pokemon in order to win the challenges in the Battle Tower/Frontier.
3) Proper EV Training will help your pokemon defeat content at lower levels than usual. The old fashioned way for most people to clear content is to just over-level against the last gym leaders, and the Elite Four + Champion to clear the game. (For example, most people would just overlevel their pokemon to levels above the game's champion (Emerald's Wallace who's highest level pokemon is at lvl58) )
4) EV Training can be done by any player and can be done as early as your starter pokemon.