Over the years, these sayings have become a ritualin the course of eating a meal. Think of it as a Japanese way of prayer.
By itself, "Itadakimasu!" is said to express appreciation for the meal prepared. But when directly translated, it is more like "Now I'm going to dig-in!" in English.
As for "Go-chiso-samadeshita!", spoken after the meal, it is said to express gratitude for the wonderful meal and for the hospitality of the person who prepared them.
An orthodox example of a Japanese meal would consist of follows: a bowl of rice, miso-soup(suimono), and 2 or 3 side dishes (the more side dishes, grander the meal).