Can someone help me understand what part 141 or part 61, etc means? Is it a training curriculum that is geared in a specific direction like corporate aviation for example?
Part 61 is the Part of the FAA regulations that govern pilot certificates, ratings, privileges an currency. With regard to instruction toward pilot certificates and ratings, it sets out fairly specific requirements for what must be covered and, to some degree, when. Within those parameters, it's fairly flexible, and all that's required is a willing student, a willing instructor, and an airplane.
141 is the Part of the regulations that controls certain types of flight schools. In exchange for FAA supervision, approval of the program, and strictly following an approved syllabus, the school can offer somewhat reduced requirements. For both the student and the school, the program is structured with a formal syllabus, including phase checks by a senior instructor, that "must" be followed.
Aside from the extremes of both is a lot of variety. There are small Part 141 programs. There are Part 61 programs that follow the same syllabus and structure as a Part 141 school.
What they are "geared for" is more a function of the school and how it sees itself than which Part it provides instruction under.