The term solid state refers to an item that performs its function without moving parts. The advantages to solid state parts are primarily speed and reliability. Moving parts add complexity to a device and are the most likely parts to fail, especially with extended periods of repeated operation. Many devices with moving parts, such as relays or switches, are guaranteed to function only up to some maximum number of cycles. Additionally, moving parts take, even at best, some appreciable fraction of a second to complete one full cycle.
Solid state parts on the other hand have no moving parts to fail, and therefore often no maximum number of cycles of guaranteed lifetime (or in cases where they do, this maximum number is much higher than their traditional counterparts). Likewise, without moving parts that must travel some distance to perform their function, solid state parts can operate at nearly the speed of electricity.
The disadvantages of solid state parts are that they require electrical power to operate, are more sensitive to certain types of stresses such as electrical shock or high temperatures, and are typically more expensive. Handled with sufficient care, however, their advantages usually outweigh these drawbacks.
Traditional relays consist of a mechanical switch and an electromagnetic solenoid. When the solenoid is energized, the magnetic field pulls the contacts to perform its switching function. Solid state relays are made of transistors and have no moving parts at all. They perform their switching much faster and eliminate the mechanical contacts that are prone to both corrosion (as sparks are generated by the separating contacts, increasing their resistance) and eventual breakage (similar to bending a paper clip back and forth repeatedly until it breaks). Traditional relays, however, can generally switch higher voltages at higher currents.
Mechanical sensors such as limit switches and float switches rely on physical contact with the object it is sensing. In extreme cases, this could interfere with the sensed object and in all cases the sensor itself has moving parts which can break. Solid state sensors such as inductive proximity sensors and capacitive sensors make no actual contact with the sensed object, being able to detect its presence at a short distance. Photoeyes also make no physical contact with the sensed object but use a very low power laser to detect its presence. Solid state sensors also tend to be more sensitive than mechanical sensors, but in some cases this is a disadvantage, as it could result in false signals. High speed operation is a significant problem with mechanical sensors, as the spring return on the switch lever is much slower than their solid state counterparts.
d'Arsonval movement meters detect electric current using magnets and springs, and display the results with a needle which moves across a chart or printed display. It is possible for the needle to get stuck if it gets dirty or corroded, and the spring will eventually wear out which at least affects its accuracy and at worst breaks entirely. Solid state meters perform their detection with precision resistors and transistors, eliminating the moving parts altogether. The electronics also make auto-ranging multimeters possible. Solid state components have so many advantages over traditional electric meters that they have completely replaced them in almost all fields.
The advantages of solid state components have been known for a long time, and were used to good effect in Robert A. Heinlein's 1941 novel Orphans of the Sky. The characters were in the generation ship Vangaurd on a centuries-long journey to Centaurus. Due to the extended nature of a trip to a distant star without using faster-than-light propulsion, the ship had to be designed to last a long time, so the use of moving parts was minimized. Even ordinary buttons were designed as capacitive or photoelectric sensors rather than mechanical buttons with springs. The zero-maintenance nature of the ship was essential to the setup of the plot: after many years most technical knowledge was forgotten (few could so much as read) and over a period of several generations even the nature of their mission was forgotten entirely — replaced with a primitive mythology that understood the ship to be the whole of creation. If the ship were built with traditional moving parts, it would have broken down within a few years of the crew forgetting how to maintain it.