SAP SE is a German multinational that makes enterprise software. It is best known for SAP ERP and its predecessors (SAP R/2 & SAP R/3). As the name suggests, SAP ERP is an ERP system, which basically means that it supports a wide range of business processes from warehouse management and sales to HR, business intelligence, etc.
Although SAP ERP isn't the only software sold by SAP, people are typically refering to SAP ERP when they say "they're using SAP at work". It's important to note, though, that SAP is the name of the company and no software is sold or licensed as just "SAP".
ABAP is a 4GL programming language created by SAP, and commonly compared with OpenEdge ABL or COBOL. Much of SAP's software is written in ABAP. SAP provides an ABAP Workbench, which is a collection of tools that allows third party developers to develop, test and run custom ABAP programs within the SAP ERP system. The ABAP Workbench is typically used only when business logic cannot be implemented in SAP ERP by means of mere configuration.