it's a sim so it's quite open ended and there are a variety of goals that you can achieve, but essentially, the game goes as follows:
each pinata has conditions to make it appear outside your garden.
each pinata has conditions to make it visit your garden.
each pinata has conditions to make it become a resident of your garden.
each pinata has conditions to make it be happy to make children in your garden.
each pinata has two tricks and three colour variants that are unlocked by it being fed specific things.
These conditions are generally "At least X amount of Y present" where Y is a pinata, a plant, a food, a decoration, or a land type or similar. Some are a bit quirky though.
Pinata will never join your garden if there are already two of that species resident, so you are forced to romance your pinata to make more than two of anything.
Now the game's designed so that one garden could never begin to romance every pinata ever (like, the horse requires 50% grass and the hippo requires 70% water), so the goal of the game depends on what you want to do. I had a garden where I just tried to make as much money as possible (I made it into a dairy/wool farm), I had a garden where I tried to have both snow and sand environments (this is in Trouble in Paradise, the vastly superior sequel. Get TIP, not the orig), I had a garden where I just tried to attract really rare pinata.
And there are some rare pinata that have really strict or costly requirements, some that don't appear but are instead unlocked by "evolving" other pinata (ie: doing odd things that you can only pick up hints about in dialogue if at all), etc. There is a lot of content and you could quite easily sink many hours into the game without even scratching the surface.
YEAH GET VIVA PINATA