So, the Desert Fathers emerge around the end of the 3rd century, beginning of the fourth. It begins as a movement of sorts centered in Egypt, but also with some similar and related trends in Syria, and the key feature is withdrawal and ascetic practice in the desert.

For my part, I link the rise of this desert asceticism with the decline of persecution after the ascension of Constantine. Now the path to being a heroic devotee of the faith is no longer martyrdom, since that path is mostly closed. So 'martyr-like' faith is re-interpreted along ascetic lines.

The most famous of the fathers is Antony the Great, who is made famous by a biography of his life written by Athanasius of Alexandria. The biography was wildly and widely popular, and so increased the profile of this ascetic and proto-monastic existence. While Antony pursued a solo ascetic life, it became typical to form monastic communities, such as the one organised by Pachomius. So you then get codification of community rules and spiritual practice.

In the later 4th century it is fairly common for leading church figures to have spent some time in monastic settings, people like John Chrysostom, Basil of Caesarea. This increased the influence of desert-asceticism on the urban church.

Why are they significant contributors? The desert fathers are really the birth of monasticism in the church, and monasticism grows to be a significant feature in late antiquity and a dominant feature through the middle ages. They shape the idea of what it means to live a truly 'religious' life, and develop a tradition of spirituality focused on private meditation and prayer, charitable works, withdrawal from the world, and scriptural practice (both scribal and recitative).