A quantity that is constant in time (does not change) is said to be conserved.
Conservation and System Specification
Before deciding that a quantity is conserved in a given situation it is important to carefully consider the choice of system. Although quantities like energy, linear momentum, and angular momentum are universally conserved, it is extremely rare to consider the entire universe as a single system. When considering a smaller system, energy and/or momentum can be transferred into or out of the system of interest by exchange with the environment.
For this reason, it is sometimes possible to specifically choose a system of more than one object that will allow for conservation of momentum or energy even when individual objects do not conserve these quantities. This trick is particularly powerful in analysis of collisions.
Conservation of Mechanical Energy
While energy is universally conserved, mechanical energy is not. Mechanical energy is a special type of energy that can be transformed into other types (thermal, radiative, chemical, etc.) without sacrificing conservation of energy overall. For this reason, mechanical energy is not always conserved, even in extremely isolated systems (such as the totally inelastic collision of two satellites in space).