In June's Journey, materials are used for constructing and upgrading buildings. You can acquire materials from Star Boxes or bonus rewards from playing Hidden Object Scenes.
There are many different materials in the game. Wood, hammer, and brick are very common and you will find plenty of them while playing the game. Paint is a little harder to come by, but it's not too rare. Porcelain, copper, glass, terracotta, and marble are precious, quite rare, and so much harder to come by.
All materials can be found by playing the game, but some take longer to find than others. Be patient and keep playing!