竹报平安 (zhúbào-píng’ān) (bamboo for fine)，this is a traditional phrase, frequently used when you are away from family for long, and sending a mail back home to tell your family everything is fine for you.
丁亥年 is a traditional style of recording years. There are 10 marks for sky (天干), and 12 marks for earth (地支), and they are grouped one by one, which is 60 groups (干支纪年). 丁 is the 4th of 天干, and 亥 is 12th of 地支.
Also you may have heard that Chinese people have a property called 属相 (shǔxiang), which is an animal standing for the year the person was born. There are 12 animals, paired with 12 地支. 亥 is paired with pig.