She is able to astrally project herself into various lands of myth. Her physical body reacts to whatever happens to her on the mythical astral plane, leaving her body cut, bruised, or sometimes strengthened once her mind and body are reunited. She can apparently leave the planet through meditation and did this once to rescue Artemis while she was in Hell.
Demeter, the goddess of agriculture and fertility, blessed Diana with strength drawn from the Earth spirit Gaea, making her one of the physically strongest heroes in the DC Universe and the strongest female hero in the DC Universe. This strength has allowed her to easily overwhelm Superman and Supergirl. She has also held her own against Darkseid. Her strength has no measurable limits and she can break the Chronus Scepter, which is universal in its destructive power. However, now Diana is the daughter of Zeus, king of the Greek Gods, so it is unclear as to how much of her power and strength is a direct result of her divine heritage. Her connection to the earth allows her to heal at an accelerated rate so long as she is in contact with the planet. However, as mentioned earlier, now that she is a demigoddess, it has been suggested that she heals extremely quickly also due to her divine heritage. In rare cases where she has been gravely injured, Diana showed the ability to physically merge with the earth, causing whatever injuries or poisons to be expelled from her body; such an act is considered sacred, and can only be used in extreme cases.
Thus although by the modern depiction her accomplishments at the time seem ordinary, in that era they were more so. Diana Prince was originally an army nurse, but quickly attained the rank of lieutenant in Army Intelligence. This was partially a creative convenience so that she could be close to both Steve Trevor and received information which she needed to pursue her superheroics. In the real world though, this role in Army intelligence, even as the secretary to General Darnell, was still a rare position for a woman to hold in society. At this time as well, the character had her only real sidekicks in her history in the form of Etta Candy and the Holliday Girls. These characters gave the Wonder Woman a degree more of levity while also allowing the writers to focus on some issues which were more related to women. When Marston left the character, the strong driving force of the character to act as a strong moral guide and role model for female readers left as well and the character became more sensitive to the forces driving the industry as whole. Thus Wonder Woman changed somewhat to a more stereotypical woman. Her main interest was not always fighting crime, but for a time it became all in the interest of keeping Steve Trevor happy and interested in her for marriage. Also the backup stories featuring the Wonder Women of History were slowly phased out and replaced with features on marriage customs from around the world and trivial facts on random household objects.