For ERP applications (which SAP is arguably most famous for) you are basically getting all of the "standard" features that you require to run a business in one highly integrated (and usually highly modular) package. This will include, at a very basic level:
- Accounting (general ledger, fixed assets, accounts receivable, accounts payable, budgeting, consolidation, maybe treasury)
- Supply chain/warehouse
- Manufacturing (processes, bill of materials etc.)
- Interfaces (including web portals, EDI, perhaps direct links to manufacturing systems)
- Many many others...
What arguably makes this all rather complex is providing all of this functionality in a way that can work across a large multi-national organisation - for example, the accounting and tax rules in different countries can be very different. Even the basic technical challenges of getting a Tier-1 ERP working in a global company are non-trivial.
Factor that these things are highly customisable and you can perhaps see why they have to be so complex.