im unsure what the brew quality in the brewing is, is that something to tell just how on top of adding ingredients I am? does it give the pet a special boost?

The brew quality tells how good the brew is doing. The higher the quality, the faster it'll progress. You keep it up using the brewing agents when the brew is in need of them.

The boosts come from keep the quality up for set amounst of time i believe. They give boosts to the pet like extra genes or stats, something like that i don't remember specifics

For Regular and Fabled catalysts, 1/2 Bonus from keeping up Quality is a stat boost, and 2/2 is a random carried trait
For Majestic Brews, both Bonuses are stats

When you tend to a brew, you return the Condition to Good and raise the Quality one stage (Normal > Good > Great > Perfect)- after a period of time (not sure what it is this fest, but usually about 35 minutes or 1hr5mins) the brew will want to be tended again.
If the brew is left unattended for an hour after this happens, the Condition will drop one stage, dropping a stage for each hour it is unattended.

Quoting the News Post but paraphrasing a little (unbolded segments in first bit are us altering the text to try to add clarity)
"There are also Quality and Bonus measurements. Preventing your Brew from having lingering Conditions and continuing to counteract Conditions will improve its Quality. If you keep your Brew at Perfect Quality, it will receive Bonus % points every hour. If a Brew fills bonus bars- up to two total- by the time it is completed, it will receive up to two special bonuses to the resulting Themed Pet! This may be a tad confusing, so I will try to break it down further.

There are four different tiers of Quality:
Normal: Slowest rate of Hourly Progress and Agent Progress towards completion. No Hourly Bonus. No Agent Bonus.
Good: Double rate of Hourly Progress towards completion. Slowest rate of Agent Progress towards completion. No Hourly Bonus. No Agent Bonus.
Great: Triple rate of Hourly Progress towards completion. Double rate of Agent Progress towards completion. No Hourly Bonus. Single Agent Bonus.
Perfect: Quadruple rate of Hourly Progress towards completion. Double rate of Agent Progress towards completion. Double Hourly Bonus. Single Agent Bonus.

...

If a Condition is ignored for too long, then every Hour a Brew's Quality will decrease by one tier until settling back at Normal.

Each Brew can unlock two Bonuses. This can easily be tracked in the list of information for each Brew. For any Brew, the first Bonus is an additional boost to the resulting Themed Pet's Statistics, equal to two additional Ranks of using Spectral Essences. For Majestic Catalysts, the second Bonus is an additional two Ranks boosted to Statistics. However, for all other Catalysts, the second Bonus is an additional Carried Trait to an empty slot."