What about Earth allows it to maintain bodies of water?

Planet Earth is currently the only one in the solar system where the presence of large body of waters on its surface is confirmed.

Other planets may have had running water on their surface in the past (Mars) or could currently have liquid oceans of water below a frozen ice crust (Jupiter's satellite Europa).

The main reasons because our planet has liquid water are:

Gravity: the planet mass is big enough to generate a gravitational field able to maintain water vapor and other gases from escaping in the outer space.

Atmosphere: the above mentioned atmosphere allows for formation of clouds, rain and it is of paramount importance for the existence of the water cycle and thus for the presence of oceans, lakes and rivers.

Temperature: the average temperature of the planet (16 Celsius) is well within the range of liquid water. In other words on Earth water will not be totally frozen, as in planets too cold, or totally evaporated, as in planets too hot. This is due to the existence of an atmosphere (acting as thermal blanket) and correct distance from the sun (not too close or too far).