Informal language is what you would use to write a postcard to your friend. Formal language is what you would use to write an article for The Times. For example:
Italy is a country well worth visiting: a fine cuisine, good wines and exquisitely beautiful countryside. (Formal)
Italy's great! Great grub, great plonk and great views. (Informal)
Formal language usually uses longer words, and a wider vocabulary, as well as sticking to more traditional grammar rules. Informal language uses more contractions, more slang and is more likely to use non-standard grammar rules.