The other answer is really terrible in terms of efficiency. Try this:
create table test
(
id int identity,
month varchar(25) , growth int
)
insert into test ( month, growth ) values ('sep' , 5)
insert into test ( month, growth ) values ('oct' , 6)
insert into test ( month, growth ) values ('nov' , 2)
insert into test ( month, growth ) values ('dec' , 9)
with growth
as
(
select month, growth, lag(growth, 1, null) over (order by id) as prev from test
)
select month, growth, case when prev is null then 'first value' when growth - prev > 1 then 'increased' when growth = prev then 'same' else 'decreased' end as result
from growth
This works for SQL Server 2012. Note that I added an id column, without that, you need to find another way to define the sort order so that you sort by month.