"Strong as a lion" means that no man should be ashamed of the people who mock him when engaged in the service of G-d, B"H.
"Light as an eagle" refers to the vision of the eye, i.e. be swift in shutting your eyes not to look at evil things, because vision is the inception of sin - the eye sees, the heart covets, and the instruments of action complete it.
"Fleet as a hart" refers to the legs, i.e. your feet shall always run swiftly to do good.
"Strong as a lion" refers to the heart, because the seat of strength to do the service of G-d, B"H, is in the heart. It is the duty of man to strengthen his heart to do His service, and to prevail over his yetzer ra, just as the hero makes every endeavor to prevail over his enemy, subdues him, and throws him down to the ground. (Kitzur Shulchan Aruch, Laws Relating to the Conduct Upon Rising in the Morning)
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Transliteration / Translation:
Pirkei Avot - Ethics of the Fathers (literally "Chapters of the Fathers"), a section of the Mishnah.
B"H - Baruch Hashem - Blessed be/is His Name
yetzer ra / - evil inclination
