Full client is an operating mode where a node maintains a complete set of data from the blockchain locally.
Depending on a chain such nodes may store dozens of GBytes of data, so it may be quite costly to maintain. On the other hand, such nodes are important for chain security and typically form the backbone of the network.
For most users, this may not be an optimal choice. Usually, light client is preferred, especially for mobile devices.
TODO: Substrate specifics.