The townsfolk may ask you to bring them flowers, minerals, bugs or other items that they want. How you find the things they are asking for depends upon the type of item. You won't always be able to find what they want, but that won't make them mad at you, and they will forget about it by the next day and probably want something else.
You will know if they still want the item they asked you for, because they will have a little "thought bubble" over their head with a picture of the item they want. If they no longer have that little thought bubble over their head, you won't be able to give the item to them. The townsfolk will only want the item they requested until the end of the day. After that, it's too late to give it to them.
Flowers and seeds:
You can sometimes find flowers growing around the town, and might find the one that you're looking for. You can also purchase 5 seeds from the General Store each day, and it's a good idea to plant them so that you have a variety of flowers growing in your town. Since flowers take a day to grow, you won't be able to grow one in time to give it to them on the day they ask for it.
You can catch various bugs in your town to give to the townsfolk who are asking for them. Different bugs appear in different areas in your town and at different times of the day. Some bugs like grass or trees, and other bugs prefer morning or night. Look around in the right place and at the right time of day and you have a good chance of finding the bug you want.
Minerals can be found by breaking open the small grey or gold rocks with the pickaxe, and sometimes townsfolk will reward you with minerals after you give them something that they were asking for. Minerals tend to be harder to find than other items, so you might not be able to find a particular mineral on the day you need it.
How do I give the townsfolk an item that they want?
Once you tap on the person to talk to them, they will acknowledge that you have the item they are interested in. The easiest and fastest way to give the item to the person is to tap on it in Inventory to automatically transfer it. If you’d rather, you can drag and drop the item onto the person who wants it. If it falls onto the ground, you will need to pick it up and try again.