Ichigo is a shinigami which means a fair number of things so I will try to sum this up as best as I can:
1) Ichigo can see ghosts. 2) With the help of his badge (or other shinigami), he can leave his body to become a shinigami (think of spirits or guardian angels). He can touch and influence things both in the spiritual as in the living world while he is in this form. So when he is in a fight, the damage he does will influence his surroundings. 3) As soon as he leaves his body, Ichigo will be in possession of his zanpakutou (aka soul cutter). This is a sword with its own mind as you will. Every shinigami has his own zanpakutou which grants him a very distinct power. Ichigo's allows him to send a blast a very high spiritual energy at his opponent (with the result of making things go boom, think lightning if you want). 4) Ichigo can reach 'bankai' which is a higher level of strength. It will make his attack described above more powerful. It will also make him very, very, fast. 5) All these skills are only available to him when he's in spirit form. When he's just him, he can't use these attacks. (He can still see ghosts and spirits however.)
Re: Inherent Abilities
1) Ichigo can see ghosts.
2) With the help of his badge (or other shinigami), he can leave his body to become a shinigami (think of spirits or guardian angels). He can touch and influence things both in the spiritual as in the living world while he is in this form. So when he is in a fight, the damage he does will influence his surroundings.
3) As soon as he leaves his body, Ichigo will be in possession of his zanpakutou (aka soul cutter). This is a sword with its own mind as you will. Every shinigami has his own zanpakutou which grants him a very distinct power. Ichigo's allows him to send a blast a very high spiritual energy at his opponent (with the result of making things go boom, think lightning if you want).
4) Ichigo can reach 'bankai' which is a higher level of strength. It will make his attack described above more powerful. It will also make him very, very, fast.
5) All these skills are only available to him when he's in spirit form. When he's just him, he can't use these attacks. (He can still see ghosts and spirits however.)