Spiritual Growth

The Hebrew term for festivals רגלים, is a derivative of the word  רגל meaning "foot".  This alludes to a level of profound commitment to G-d where one is not merely serving his Maker due to one's understanding, or due to one's spiritual sentiments, but rather, out of simple obedience, like a "foot soldier".

On the other hand, the festivals are also associated with joy, where a person's positive feelings towards G-d take outward expression.

What is the connection between obedience and joy?

The answer is hinted to by the fact that the Torah fixed the festivals according to the agricultural cycle.  In order for a seed to grow, it must first shed its outer shell, and only through this is the seed able to grow many hundreds of times in size.  Similarly, when a person puts aside ("sheds") his superficial preconceptions ("shell") about Judaism and observes all the mitzvot with absolute loyalty, he will experience an enormous spiritual growth.

And likewise, a person who serves G-d with joy which "breaks all boundaries" will experience an unrestrained spiritual growth.

Source: Based on Likutei Sichot of the Lubavitcher Rebbe