It is a little like a string on a guitar. When you hit the string, based on its mass, tension, and the distance between the two supports (electrically equivalent to short circuits), it rings with a single pure audio note. The length is half wavelength in that case, since the string passes over a support, goes quarterwavelength down the string where it is vibrating the most, and then goes another quarterwavelength down until you hit the second support.
In RF, an antenna typically has an open circuit at one end. So, you start at a low impedance point (the antenna base), move quarter wavelength up the antenna to a point where the electric field is oscillating the most, and end in an open circuit.
In the electrical case, if the antenna continued on past the quarter wavelength point, the next resonant case would be if the antenna was a half wavelength long and the end was short circuited (like in the guitar string example).