Non-combat skills are miscellaneous skills that are unrelated to the combat-related skills. You can find your non-combat skill levels as well your combat-related skills in the attributes menu by pressing the "F" key. Amongst the currently functioning skills are Thieving, Merchanting, and mining.
Thieving is the ability to steal random stuff from citizens and guards be sneaking behind them and then right-clicking. At level one, player can steal from citizens. At level five, players can steal from guards.
Increases the amount of money recieved from the sell merchant and is improved every time you sell him something (may not be immediately visible).
Mining is the ability to mine ores and requires a pickaxe, which can be bought from the miner in Port Juno. Each time a certain level is reached, the player can mine better ores, use better picks, and enjoy faster ore respawn time from the ore spawners.
Smithing has not been implemented yet, but will probably consit of making ores into bars.
Manufacturing has not been implemented yet, but will probably consit of making bars into armor, weapons, or tools.