Short meaning: The strength card represents strength in a positive way, often personal strength in adverse situations. Sometimes the card represents physical strength.
Full meaning: In some Tarot decks, Strength is card number eleven of the Major Arcana, and Justice is card eight. Waite used the eighth position for Strength, and because the Rider-Waite deck is so popular in the U.S., I'm using his numbering system here. Hollander (see Sources) claimed that older decks typically used number eleven for Strength.
The Strength card is also called the fortitude card, and most descriptions of the card include terms like courage, resolve, focus, self-confidence, self-control, patience, triumph, determination, perseverence, compassion, or creativity. An attribute of gentleness and wisdom seems to be a theme among authors. A few authors have also written that a love of animals could be represented by this card, or the card could represent animals because it typically shows the image of a lion.
Dee (see Sources) provides a good definition in his book:
"The card is governed by the sign of Leo, indicating honor, reliability, honesty, and a fixed sense of purpose.
"This card is a good indication of recovery from illness or other difficulties. It may describe a situation that must be reacted to bravely even though you are afraid. Resolute action and a willingness to stand up for what is right no matter what the consequences are shown by the card.
"Meaning: Physical strength, courage defeating mean attitudes and hatred. You will triumph over your enemies. If ill health has been experienced, then rapid improvement will occur. A fight for fair play." (Dee, p. 14)
Hollander describes the card as representing a "Force of will, moral strength. Personal vitality. Courage, triumph. Fortitude, determination, energy, defiance. Ability to endure hardship. Success."(Hollander, p. 65)
The Strength card reversed generally means a lack of strength, problems surrounding personal strength, or an abuse of power.
Dee described Strength reversed as "Cowardice, loss of nerve. Giving in, or being beaten by unfair means. You must overcome your own fears to find inner strength." (Dee, p. 14)
Abraham attributed some negative personal characteristics to Strength reversed: "Lacking the strength to overcome difficulties in life. Little self-control. Egotistical, loud, and vain. Lazy or overly ambitious. Limited knowledge regarding inner resources. Active sexual life. Not a trustworthy friend due to jealousy or dishonesty. A follower, not a leader. Ruthless in positions of power." (Abraham, p. 101)
Martello wrote that Strength reversed can represent an abuse of strength or power: "Disharmony, abuse of power, tyranny, attempt to use force to gain one's ends, dictatorial, chauvanistic, domineering, lacking self-control." (Martello, p. 46)