In what ways does mindfulness relate to Jewish observance and practice? I believe the idea that a person be fully aware of what he or she is doing and appreciate it is central to Jewish practice and observance, and is the epitome of kavannah.

The Gemara discusses the principle אין עושים מצות חבילות חבילות we do not double up and bundle mitzvos together and perform them at the same time. Therefore, if one was in a meal that carried into a Shabbos or Yom Tov eve, one may not use the same cup of wine that is used for the recitation of bentching for the recitation of kiddush. The Gemara Sotah (8a) discusses more applications. 

What is the basis for this principle? There are different opinions with slight psychological nuances. 

• Rashi (Sotah 8a) tells us that it is disrespectful for the mitzvos, as it appears as if they are a burden to be efficiently dispatched. 
• Shevet Musar (23:1) says that one cannot concentrate properly on each mitzvah if they are combined simultaneously. 
• Darchei Yesharim (Hanhagos Yesharos 38) adds an interesting twist: We should not bundle the mitzvos so we are able to perform them with joy. We need time to rest between one mitzvah and another. (Presumably, he means that we need to reflect and pause between each mitzvah to better appreciate it, similar to pausing between courses in a meal.)
• An extension of this idea comes from the Arukh HaShulkhan (O.H. 546:1) who compares the principle of אין מערבין שמחה בשמחה we did not mix one joy with another to אין עושין מצות חבילות חבילות. The prohibition to marry during a festival is the same as the prohibition of bundling mitzvos together. In both cases, the lack of time to reflect and allow for each experience to become distinct, saps the ability to feel the fullest form of joy that otherwise would be available. 

All is these ideas, particularly the last one, underscore the importance of mindfulness to realize joy in life and observance of the commandments.