During the Substitute Shinigami arc, it is covered that both Ichigo and Ginjo are Substitute Shinigami (Ginjo being and ex-Substitute Shinigami). How does one become a Substitute Shinigami, what does this title bring with it, and why is Ginjo no logger a holder of said title?
According to the Bleach Wiki:
A Substitute Shinigami (死神代行, shinigami daikō) is someone who became Shinigami by obtaining another Shinigami's power, or by going through a much harder and riskier process to transform him/herself into one.
Ginjo was the first Substitute Shinigami that was recognized as such by the Gotei 13. The origin of his powers is unknown but according to Captain Soi-Fong he murdered many shinigami to get his powers.
Ichigo, on the other hand, received his powers from Rukia Kuchiki when she gave him a portion of her power by the method of endowing her zanpakuto with said power and stabbing Ichigo with it, in order to protect his family.
If a Substitute Shinigami appears, Soul Society gives that Shinigami a special badge which they use to monitor and restrict the Substitute. However, the Substitute is told that it is a license which is given to Substitutes that prove beneficial to Soul Society to allow them to do their work and identify them as a Substitute. The badge alerts the user if Hollows are nearby via an alarm sound which can only be heard by the owner and the item itself is only visible to other spiritually aware beings. The Badge can also allow the soul to leave the body.
Ichigo received his badge after he went to SPOILER invade the Seireitei to rescue Rukia from being murdered on account of her giving power to a Human. The Gotei 13 saw the sheer power Ichigo possessed and recognized him as a Substitute Shinigami so they make keep an eye on him and call on him in times in need (Personal opinion which preceded to be the spine of the rest of the series's plot).
Ginjo received his badge for a similar reason, so that the Gotei 13 could watch his actions (specifically so he would not murder more Shinigami to gain power) and to call on him in times of need.SPOILER In time he realized the real purpose of the badge and feeling betrayed he disappeared from the Gotei 13's radar without a trace.