Short answer
Town Gratitude is the golden thumbs-up at the top of the screen, and sermons need it. The cap starts at 10 and rises to 20 after the first battle opens the port. Reliable sources are quest rewards (+5 sheets), burial certificates at the tavern, selling in-demand goods, battles and, biggest of all, Town Warehouse orders at 15 to 25 each. Raise the cap further by repairing town buildings and inviting residents through Linda.

The graveyard
View full-size image ↗Official promotional screenshot · © Lazy Bear Games / tinyBuild · Official media kit · Material credits
What Gratitude does
Gratitude is shown as a golden thumbs-up at the top of the screen and is needed to perform sermons in church.
Sermon success is driven by the lower of your Gratitude and the church's rating, so a beautiful church cannot make up for empty Gratitude.
Fextralife describes the Town Gratitude item as granting 5 Likes, which is why guides use the two terms almost interchangeably.
The cap: 10, then 20, then more
The maximum starts at 10.
Winning the first battle and reaching the port raises it to 20.
Beyond that, repairing buildings in The Town with Building Kits and other materials raises it, and so does inviting new residents.
Visit Linda at the Dockside Club on Lust day once the population grows; each invitation raises the maximum by one or two.

The Town harbour in the official media kit. Reaching the port is what raises the Gratitude cap to 20.
View full-size image ↗Official promotional screenshot · © Lazy Bear Games / tinyBuild · Official media kit · Material credits
Where Gratitude comes from
Main and side quests hand out Town Gratitude sheets worth +5 each — plentiful early, limited later.
Burial certificates sold at the tavern give +1 each; one guide found this capped at 5 per week.
Selling in-demand goods such as wheat, fish and vegetables to the Merchant, or goods to specialised merchants, also pays in Gratitude.
Battles reward it too: city battles give 4 or 8 Town Gratitude each, depending on the fight.
Warehouse orders are the big one
Completed Town Warehouse orders pay 15, 20 or 25 Gratitude, more than any other single source.
They need packed Supply boxes and are only taken on Pride day — our town orders guide covers the details.
When you are short before a sermon
The tavern sells Gratitude directly: 5 silver for +5.
One community guide describes a cheaper buy-and-sell loop with the trader Herm: buying fillets, wheat and vegetables and selling them back returns 10 Gratitude for a net cost of about 2 silver 26 copper per week.
The same guide notes unused Gratitude does not carry over, so there is no point stockpiling beyond the week's sermon.