Being a legacy holds a lot of weight, as a legacy is a Powered who gets their abilities from their family line. They are individuals who are born with the powered gene active in them, though their powers don't actually activate usually until puberty or an outside danger triggers it. The vast majority of the legacies are the children or grandchildren of gold, silver, or iron age heroes, taking on the family name. Most of the time, they tend to have the same powers as their family members, like Zero, a modern hero who took on the name and powers from his grandfather who fought during World War 2 as Zero. Other times, the powers are closely related, like Beat and his daughter Scratch who can manipulate sound and silence respectively.
The term "legacy" is an internal term for the Powered community, as to the normal world, a legacy hero is any hero who takes on a pre-existing persona. Any sidekick who takes on their mentor's name is a legacy to the public, but if a Powered tells you that they're a legacy, it means that they were born with their powers.