BREAKPOINT
First of all, the concept of break point does not confined only to SQL SERVER rather it applies to many programing language environment(like dotnet).
However,
A breakpoint, in software development, is an intentional stopping or pausing place in a program, put in place for debugging purposes. More generally, a breakpoint is a means of acquiring knowledge about a program during its execution. During the interruption, the programmer inspects the test environment (logs, memory, files, etc.) to find out whether the program functions as expected.
In practice, a breakpoint consists of one or more conditions that determine when a program's execution should be interrupted.
The most common form of a breakpoint is one where the program's execution is interrupted before a programmer-specified instruction is executed. This is often referred to as an instruction breakpoint.
Other kinds of conditions can also be used, such as the reading, writing, or modification of a specific location in an area of memory. This is often referred to as a data breakpoint, or a watchpoint.
Breakpoints can also be used to interrupt execution at a particular time, or upon a keystroke etc.
The above content is obtained from
Breakpoint
Since Sql Server 2008, Transact SQL Debugger is incorporated with SQL Server Management Studio there by giving the privilege of debugging Transact SQL statements line by line, using
breakpoints, step into, step over, step out from database programming objects(stored procedure, function, triggers etc.)
Look into
New Features in SQL Server 2008 Management Studio – Part 3 for obtaining a more clear picture.
In short and simple
breakpoints are use for program debugging IntelliSense
The best and sweet description I could present to you is
IntelliSense
Intellisense (a feature of SQL SERVER 2008) reads the internal metadata and provides users with a list of available objects and properties while the code is being written. Prior to SQL Server 2008 this feature was supported only by third party products. The Intellisense feature in SQL Server 2008 helps database developers to write the TSQL code effectively, especially those not familiar with the syntax.
You can enable or disable this feature either from Query | Intellisense Enabled or enable or disable this feature by clicking Intellisense Enabled button from the SQL Editor Toolbar.
Look into
New Features in SQL Server 2008 Management Studio – Part 1 for more information
7
