Supreme Court is the highest court of the land, and normally the court of last resort, the final court of appeal.
Supreme Court hears appeals against the decisions of High Courts in its appellate jurisdiction. Under Article 136 of the constitution It can also hear grievances as to any order by any court or tribunal in the country if the same is tainted by illegality. Since this is an exceptional power – the court normally refrains from interfering unless other equally efficacious remedies like approaching the high court have been exhausted, and while entertaining an SLP (Special Leave Petition) the court won’t sit as a regular court of appeal and won’t go into questions of fact, but only inferences to be drawn of existing material and evidences.
Hence we can see that jurisdiction of SC is primarily appellate. But that does not mean it has no original jurisdiction, it has original jurisdiction in disputes between states. Citizens can also approach the SC even directly in cases where fundamental rights are violated under Article 32 of the constitution. (Also called extraordinary writ jurisdiction).
The court has over the years relaxed strict rules of technicality while dealing with Public Interest Litigations. And even a letter or email can get the court to initiate enquiry into alleged violation of fundamental/human rights.
The SC also exercises jurisdiction in inter-state transfers of criminal/civil matters.