This a term for solder which becomes liquid and solid at the same temperature. How is this possible?
An explanation is given by Wikipedia:
" … each pure component [of a homogeneous mix of materials] has its own distinct bulk lattice arrangement. It is only in this atomic/molecular ratio that the eutectic system melts as a whole, at a specific temperature (the eutectic temperature) the super-lattice releasing at once all its components into a liquid mixture. The eutectic temperature is the lowest possible melting temperature over all the [possible] mixing ratios for the involved component species.
Upon heating any other mixture ratio, and reaching the eutectic temperature, … one component's lattice will melt first, while the temperature of the mixture has to further increase for (all) the other component lattice(s) to melt. Conversely, as a non-eutectic mixture cools down, each mixture's component will solidify (form its lattice) at a distinct temperature, until all material is solid."
When soldering with 63/37 solder, the solder is heated above its melting (liquidus) point and so remains liquid for a short time until is reaches its solidification temperature. The important element is that this is the lowest temperature that a mixture of materials can melt. In the case of lead/tin solder, it 183C. Other solders have different eutectic temperatures, e.g., a 96.3% tin and 3.7% silver solder has an eutectic point of 221C.