Gourds and Slayer Progress
A gourd is an item you buy from Ren at Butterfly Estate and blow into. Each Large Gourd adds 300 to your Slayer Progress bar, which has four levels: levels 2 and 3 add health and stamina, and level 4 adds more health and unlocks a speed skill called Breathing Boost. The bar belongs to Slayers, so you need Final Selection behind you.
Opening Ren’s shelf
Ren stands by a shelf of red gourds outside a building at Butterfly Estate. Before he sells anything he wants his lost sword back: the quest Locate Ren’s Lost Nichirin. The blade lies northwest of the estate, down and across the river, near the waterfall. Bring it back and the shelf opens.
The quest may need level 75.

Ren's errand: Locate Ren's Lost Nichirin 0/2, Nichirin Blade found 0/1, Return to Ren 0/1, Exp +5,805 (1.29x), Wen +495.
Three sizes, and why only the large one counts
Small Gourd
800 Wen
Reportedly +25 progress each: 32 Wen per point.
Medium Gourd
3,000 Wen
Reportedly +100 progress each: 30 Wen per point.
Large Gourd
8,800 Wen
+300 progress each: 29 Wen per point.
Fill the bar with Large Gourds. The small and medium ones likely cost more Wen per point, so there is no saving in them. The shop has a quantity picker, so you can buy a stack at once.

Ren: Would you like to purchase 'Small Gourd' for $800 each?, with a Custom Amount picker.

Would you like to purchase 'Medium Gourd' for $3,000 each?

Would you like to purchase 'Large Gourd' for $8,800 each?
Buying is not enough: blow into it
The bar only moves when you use the gourd. Equip it from your inventory, then hold left click (hold the screen on mobile) to blow into it; the gourd is spent and +300 Slayer Progress pops up. Buying alone leaves the bar where it was.

Right after buying: Slayer Progress Lv 1, the bar at 325 of 2,000, and a Large Gourd pickup notice. Buying alone does not move the bar.

Blowing into it: +300 Slayer Progress, twice.

Large Gourd, Rare: Large Estate gourd for practiced lungs. Blowing it out spends the vessel and advances Slayer breathing discipline.
The four levels
Lv 1
2,000 to fill
No bonus yet
Lv 2
3,000 to fill
+15 Max Stamina, +50 Max Health, +0.05 Max Health Factor
Lv 3
7,000 to fill
+25 Max Stamina, +75 Max Health, +0.07 Max Health Factor
Lv 4
Max
+100 Max Health, Breathing Boost, +0.08 Max Health Factor
Leftover progress rolls into the next level, and the first level-up also paid 2,000 experience and 1,800 Wen. From an empty bar that is 12,000 progress, or 40 Large Gourds for 352,000 Wen. With some progress already on the bar it can be as few as 37 gourds, about 325,000 Wen. Each level’s bonus may add to the last or replace it.
To reach Lv 4
40 Large Gourds
352,000 Wen at Ren’s price, for 12,000 progress.

Lv 2 125 / 3000: +15 Max Stamina, +50 Max Health, +0.05 Max Health Factor.

Lv 3 300 / 7000: +25 Max Stamina, +75 Max Health, +0.07 Max Health Factor.

Lv 4 (Max): +100 Max Health, Breathing Boost, +0.08 Max Health Factor.

+300 Slayer Progress Lv 1 → Lv 2, +2,000 Exp, +1,800 Wen.
Breathing Boost
At Lv 4 the skill lands on the N key by itself; it is not in the skill tree. It gives a burst of speed with a golden glow that lasts somewhere between a couple of seconds and a minute, possibly about 15 seconds.
Demons do not get this bar or the skill. They get a Demon Progress bar in the same menu, filled with souls instead of gourds, and its level 4 adds stats only. Other ways to spend Wen once you are a Slayer are on the leveling page.
Slayers 2 How To Get MAX SLAYER PROGRESS + Breathing Boost Fast + Full Guide! (NEWCODES)
The bar at its cap, Ren's errand, and Breathing Boost on the N key.