Specialist cells (Statocytes) in plants are able to sense gravity. Thus shooting tips grow upwards, against the Earth's gravitational field, while roots grow downwards.
Statoliths are dense amyloplasts - organelles that synthesize and store starch involved in the perception of gravity by the plant (gravitropism). They collect in specialized cells called statocytes. Statocytes are located in the starch parenchyma cells near vascular tissues in the shoots, and in the columella in the caps of the roots.
“How amyloplast sedimentation is sensed within the root statocytes remains unsolved, however. It is possible that sedimenting statoliths might contact receptors embedded in sensitive membranes on the side of the statocyte, thereby triggering gravity signalling within the cell (Braun, 2002).”
source: Gravity Signal Transduction in Primary Roots
There is also evidence (primarily from experiments in zero-gravity) that so called 'non-professional' cells can also somehow sense gravitational fields. As yet this is also unexplained. The same seems to be true of many other types of cells in fungi, and even animals.
“Sensing gravity by ‘non-specialized’ cells is still puzzling. We don’t know where or by which mechanism such cells sense gravity. These questions in ‘gravisensing’ are not much different from questions in general mechanobiology. Numerous studies have been reported in this field in the last couple of decades. What are the mechanical properties of a cell? Are there differences in mechanical properties between cell types and if so why?”
Source; Mechanomics and Physicomics in Gravisensing in Microgravity Sci. Technol (2009) 21:159–167
A set of experiments performed in France in 2017 showed that plant shoots, which are traditionally thought-of as showing (negative) gravitropism by growing upwards, may not in fact be responding to the influence of gravity at all.
Using a centrifugal device combined with growth kinematics imaging, we show that shoot gravitropic responses to steady levels of gravity in four representative angiosperm species is independent of gravity intensity. All gravitropic responses tested are dependent only on the angle of inclination from the direction of gravity. We thus demonstrate that shoot gravitropism is stimulated by sensing inclination not gravitational force or acceleration as previously believed.
See: Inclination not force is sensed by plants during shoot gravitropism Scientific Reports 2016; 6: 35431.