You must acquire Fodder when caring for monsters in Rune Factory 5. Fodder is what monsters eat, and it isn't as easy to come by as you may be used to with other farming sims. In fact, you may not even know where or how to get Fodder at all.
Once you build your first Monster Barn and complete Ryker's request to do so, you will unlock the ability to buy Fodder. The item will now be sold at the General Store, but there is a small catch: you have to grow the Fodder. You can't just buy it in bulk and give it to your monsters. You will need to purchase the seeds and then tend to the crop every single day.
Related: Rune Factory 5 Gift Guide
Fodder doesn't take long to grow, so you only need to wait four days to have a stock of it. The seeds will run you 30G each, so they aren't going to break your bank, either. Fodder is a crop that doesn't need to be replanted, and the plant will continue to grow after each harvest.
For more on Rune Factory 5, check out Where to buy Flower Seeds in Rune Factory 5 on Pro Game Guides!