Elongation is the percentage of its length that something will stretch before it breaks.
During tensile testing to see how much stress (force) it takes to break a material, the material rarely stays the same length. As the load increases, the material stretches, like a rubber band would.
Sooner or later, the material breaks. The amount of stress needed to break it gives us the tensile strength value. The percentage of length it grew gives us the elongation percentage value.
A material that is ductile will stretch or change shape because its elongation value is high.
A material that is brittle will stretch or change shape very little because its elongation value is low.
The other material property that is important is the Yield strength.
When a material is subjected to stress (force) it will usually stretch or deform to some degree.
As the stress is increased the material will stretch or deform more.
There is a limit to how much force it can take though before it becomes permanently stretched or deformed.
For instance you can bend a piece of wire by applying a force (stress) to the side of it.
Up to a point, the wire will "spring back" to its original shape and size. If too much pressure is applied the greater stress (force) will bend the sire and it will only partially spring back.
The amount of stress (force) needed to reach this point of no return is the Yield strength value and in the case of the permanently bent wire, that yield strength has been exceeded.
Usually, materials with good elongation properties yield long before they break (reach their tensile strength limit).
Materials with poor elongation properties often show little sign of yielding before they break.
An odd thing about most materials.
Repeated applications of stress (force) tends to make them more brittle. Their elongation value is reduced slightly with each application.
If their elongation value is high it takes a long time for this to cause a problem.
If the elongation value is low it can cause problems fairly rapidly.
The closer the stress value is to the yield strength and tensile strength of the material, the more rapidly this embrittlement occurs.
This is one of the reasons a "safety factor" is always used in designing a gun barrels wall thickness.
Fortunately for us, the actual stresses in our barrels when firing a muzzleloader are far below the yield and tensile strength of the weaker carbon steels and their elongation is high enough that shooting them doesn't create a problem by changing the barrels elongation value.
There is no doubt about it though, if a materials elongation value is higher, there is less likelihood of the barrel failing.