The events vary and include collecting limited time supplies to craft seasonal items and collecting rare creatures in your garden to be rewarded with exclusive gifts. (darkainarts.com)
As is evidenced just by the responses from individuals on this thread alone, we are far from being as rare a creature as some might believe. (rachelheldevans.com)
Once you've caught them, you can share rare creatures with other players, in their gardens. (perfectly-nintendo.com)