It is Agile methodology not agile testing.

Agile methodology is one of the latest SDLC like Waterfall, 
V, spiral, Incremental, Prototype.....

In Agile methodology, the software is delivered in patches 
in very short time, like every patch is delivered in 90 
days time. 

The testing starts parallely with the development of the 
first patch and the first patch with complete development 
and testing is delivered in first cycle that is 90 days 
time.

When the development of the second patch starts, regression 
suite is run on the first patch to make sure that what was 
woking earlier is also working now.

In Agile methodology,the teams work as 'Scrum' team.
The advantage of 'Scrum' team is every Design team will 
have a one member from Dev and test team, similarly every 
dev team will have a member from Design and test team, 
Every Test team will have a member from Design and dev team.

The advantage of this is:-
If the dev team has any query, it need not wait for the 
design team to respond as their team has a member from 
the 'Design' team.

if the Test team has any query it need not wait for the dev 
team to respond as their team has a member from the 'Dev' 
team, so lot of time is saved.

Advantages of Agile methodology:-
Agile methodology drastically reduces testing cycle time as 
the testing is done parallel to the development activities.

The Product/Application is delivered in very short time.

Automation is must for Agile methodology as without 
automation it is not possible to run complete regression 
pack on all the patches.

Regards,
Imthiyaz. Shaik