What is BREAK and CONTINUE in ABAP?

BREAK and CONTINUE are Macros.
BREAK UserId -> This Will set user specific break point.
You can check the code for this macro in table TRMAC in SE11.
* USER specific BREAK-POINT
IF sy-uname = '&1'
break-point
ENDIF.

CONTINUE -> The CONTINUE statement can only be used in loops. If it is used, the current loop pass is ended immediately and the program flow is continued with the next loop pass.
Code in Macros (TRMAC table): (Available in NW 7.31)
* simulate continue-statement
CHECK 1 EQ 0.

Refer below snap for more details.

Now, What is Macros?
Macros enable source code to be modularized within an ABAP program. They are
• Defined between the statements DEFINE and END-OF-DEFINITION and included by their name being specified.
• Any number of ABAP statements can come between the statements DEFINE and END-OF-DEFINITION, except for DEFINE, END-OF-DEFINITION, and program-initiating statements. These statements form a source code section that can included under the name macro. The definition of a macro is not bound to the limits of processing blocks.

Notes
• Breakpoints cannot be inserted into macros and the statements of a macro cannot be performed as individual steps in ABAP Debugger.
• Apart from in the code text of a program and in type groups, macros can also be stored as cross-program macros in the table TRMAC. However no new macros should be defined in the TRMAC table. Example in TRMAC – ‘RP-EDIT-NAME‘