The point of closest approach is called perihelion. These terms are specific to a body orbiting the sun. For satellites of Earth (including the moon), the points of farthest and closest approach are called apogee and perigee, respectively. The generic terms for farthest and closest approach of a body in an elliptic orbit about a larger body are apoapsis and periapsis, respectively.
The diagram below shows the times and positions of the Earth during the solstices, equinoxes, perihelion and aphelion as it orbits the sun over a year.
A common misconception is that seasons are caused by our distance from the sun. At aphelion Earth is 1.0167 Astronomical Units (AUs) or 152,096,000 kilometers from the sun and during perihelion it is 0.9833 AU or 147,098,290 kilometers from the sun. But the times of greatest solar radiation on a hemisphere happen not because of the distance between the Earth and sun but the tilt of Earth’s rotation axis. These times are during the December and June solstices.
David Dickinson observed the sun with his own telescope during perihelion and aphelion in 2012 to create the above images. They show the sun from Earth on January 4th (perihelion) and July 4th (aphelion.) You can read more about his observations as well as perihelion and aphelion in his July 2, 2013 post on Universe Today.