It is the personal identification attached to that person. Every account in FamilySearch has one. It is sometimes referred to as PID.
Further to what 'Patricia' has already proffered ...
That "L51Y-5JX" is a 'FamilySearch Person Identifier' the acronym for which is sometimes (and often) known as a PID in relation to "Family Tree" of 'FamilySearch' stands.
It is a UNIQUE Seven Digit identifier ( xxxx-xxx ) [ where those digits can be, either, alphabetic letters; and/or, numeric numbers ] for each and ever individual/person in "Family Tree" of "FamilySearch" - no two individuals/persons have the same PID.
The "System" AUTOMATICALLY assigns those UNIQUE identifiers to individuals/persons when they are "Created" in "Family Tree" of 'FamilySearch'.
Every individual/person in "Family Tree" of 'FamilySearch' has a UNIQUE identifier - no two individuals/persons have/get the same UNIQUE identifier - a UNIQUE identifier ONLY "Ever" represents ONE individual/person.
Here is a "Knowledge Article" in "FamilySearch":
What are ID numbers used for in Family Tree?
I hope this helps.
Note that not all PIDs are seven digits. Some have more. The system is designed so that they can expand the number of digits as they need more.