CREATE TABLE #TEST
(
Id INT,
Name VARCHAR(10)
)

Insert Into #Test
select 1,'A'
Union All
Select 1,'B'
union all
Select 1,'C'
union all
Select 2,'D'

Below is the output of above table,As you can see Id Column is repeated three times..

Id   Name
1    A
1    B
1    C
2    D

Now Lets check the output using simple order by..

Select Top (1)  Id,Name From 
#test
Order By Id ;

Output :(Output of above query is not guaranteed to be same every time )

Id   Name
1    B

Lets run the Same query With Ties Option..

Select Top (1) With Ties Id,Name
 From 
#test
Order By Id 

Output :

Id   Name
1    A
1    B
1    C

As you can see SQL Server outputs all the Rows which are tied with Order by Column. Lets see one more Example to understand this better..

Select Top (1) With Ties Id,Name
 From 
#test
Order By Id ,Name

Output:

Id   Name
1    A

In Summary ,when we use with Ties Option,SQL Server Outputs all the Tied rows irrespective of limit we impose