When you use a lightsaber of your own construction, the lightsaber is supposedly most attuned to your own life signature in the Force as compared to other lightsabers. How does this work, and what benefits are there to such an attunement? How significant are the differences between using the lightsabers of others as compared to your own?
This is discussed at some length in the semi-canon sourcebook; The Jedi Path: A Manual for Students of the Force. Notably there's no mention of the blade's crystal being "attuned" to the user in any way.
There do appear to be sensible reasons though:
There is a symbolic element to building one's own lightsaber. It marks you out as a Jedi that has come of age. This has strong echoes of Vader's vicarious pride at Luke's achievement in ROTJ.
It offers the opportunity to construct a saber that is uniquely theirs and matches their fighting style. Most will settle for a standard saber, but this is your opportunity to build something unusual. The manual mentions out-sized weapons, curved handles, double-blades, etc.
Jedi periodically lose or damage their sabers. Knowing how to build one means that you gain an insight into their design, repair and long-term maintenance.
As far as I know, the canon source that concerns this topic the most is the Young Jedi arc of The Clone Wars. No specifics are mentioned, such as lightsabers being "attuned to your own life signature", but in the episode A Test of Strength the weight of determining the style for a Jedi's individual lightsaber is emphasized to some degree. Certainly, the style of lightsabers vary a great deal depending on the Jedi. For example, Ezra Bridger's lightsaber can be said to fit him well, and it can be assumed that he therefore performs better with it.
From a weaponry standpoint, it allows you to build the weapon to the exact dimensions of your hand and fingers. Button placement, dial pressure, everything designed exactly the way you want it to instinctually work. My understanding is that ancient swords like katanas were forged to the owners measurements- something like the length being a multiple of the length of the forearm which meant that they would have the precise control over the weapon desired.
This is the case with anything bespoke though, from clothing to technology. If you ever want to see an example, ask a friend who built their own mechanical keyboard about the process and sit back for an hour or two. You can get into mysticism is you like, but really there is much to be said for creating something such that it both fits you exactly and you know intuitively what its strengths and weaknesses are.
Mental clarity in combat
Lightsabers contain kyber crystals, which have unique properties related to their connection with the Force. According to the Databank, the kyber crystal in a lightsaber helps provide clarity in combat. This is explicitly attributed to the Jedi having built the lightsaber with a crystal that they found themselves:
At the heart of every Jedi lightsaber is a kyber crystal found on several planets, most notably the icebound caves of Ilum. This crystal is attuned to the Force, and connected to a Jedi Knight on a deeply personal level. In this way, a lightsaber is an extension of a Jedi’s Force awareness. Because Jedi let the Force guide their selection of the crystal, the vibration that the crystal creates in the lightsaber blade helps Jedi center themselves and find balance in the Force. In this way, a Jedi can center his or her attention beyond the distractions of combat.
While that is the main benefit, obviously there are others. For example, building one’s own lightsaber ensures that the weight, material, and shape match one’s own physical characteristics and preferences. Yoda, for instance, wielded a shorter lightsaber than average, which would be easier for him to wield than a standard lightsaber:
Yoda’s lightsaber was smaller than a standard Jedi lightsaber, befitting his shorter stature.
According to this posting, there is a ceremony called The Gathering in which, Palawan's "find a kyber crystal attuned to their Force presence on the Crystal Caves of Ilum". So there may be two issues involved: 1) building it yourself, and 2) building it with a crystal attuned to your Force presence.