In my experience the term "training" is generally used to describe teaching, practicing, and reinforcing something physical or behavioral rather than an imparting of academic knowledge or wisdom.
Physical training like "training at the boxing gym" or "training for a marathon" can be equally applied to "training to kneel in a pleasing manner" or "training to give head."
Behavioral training is simply the creation and maintainence of desired behaviors and responses through the consistent use of incentives. A person might be trained to always speak in a certain manner, or react immediately to commands in a desired fashion.
Whether training is something you "need" depends entirely on you, your partner, and what you want from one another. It really is different for every couple (or group, shout-out to the polys) because every individual wants and needs different things.