A Dueling Spirit is an item you can earn by sacrificing items or dueling opponents . Your spirit can earn Sacrifice (similar to experience) which can eventually let you earn an Artifact.
You can duel opponents whilst enabling your Dueling Spirit. If you win, your Dueling Spirit's Sacrifice level will increase, however, if you lose your Dueling Spirit can lose Sacrifice. This is the most efficient way to level your spirit but has the risk of losing Sacrifice.
You can also sacrifice items you have collected to level your Dueling Spirit. The more rare the item, the more Sacrifice you will contribute towards your Dueling Spirit.
Artifacts are rewards obtained from levelling your Dueling Spirit. They can reward you with various bonuses, such as skill tree passives, force powers, stat bonuses, and more.
When your Dueling Spirit has obtained enough Sacrifice, you can ascend your Dueling Spirit's level. Artifacts can be obtained once reaching the required Ascension level with your Dueling Spirit.
When you ascend your spirit, you have a random chance to gain an artifact. This chance is increased in relation to the amount of surplus energy you have stored in the spirit.
E.g. Your spirit requires 1,000 energy to ascend. If you ascend after earning 1200 energy, you will have a greater chance to earn an artifact.