These types of calls for attention happen every so often. They're not a critical attention request; he's not ill or starving, etc. It's more of a "Hey human! Are you still there? Don't forget about me!" beep. Almost any reaction from you, even simply checking his stats, will satisfy him. There are several Japanese messages that may appear in the speech bubble. They're usually just suggestions of what you can do if you're getting bored, such as "play with me", "dress me up", "take me shopping."
When you visit the park on the first day of each month, between 10 AM - 2:59 PM you may meet the EcoUsatchi Triplets, and have a chance to gain an Eco item. There are three Eco items available. The Eco-Bag gives you a 50% discount off items purchased from TamaDepa, the Eco-Fork gives you a 50% discount off snacks purchased from TamaCafe, and the Eco-Chopsticks give you a 50% discount off meals purchased in the Restaurant.
