In 3 words: Slow, Focused, Investigative
Pressure: light, medium, firm, deep
Expect these massage strokes: long holds, slow & sustained pressure, tissue folding & sifting, pin & stretch, working around bony landmarks & joints.
Compounding effects:  Reduced fascial adhesions (aka knots), improved range of motion, reduced pain in movements, and improved tissue 'glide'.
My thoughts on Deep Tissue: "Deep" is an anatomical term referring to deeper layers of muscle and fascia tissue, not necessarily to pressure
In a true Deep Tissue massage, the smart way to work is by applying 3 principles: 
1, Work superficial to deep.
2, Work 3-dimensionally.  
3, Work slowly - tissue takes time to melt.
Getting to deeper layers of tissue can be kind of like trying to dig a hole in the ground.  
When the ground is hydrated and soft, the job can be easier.
When the ground is dry and hard, it can be next to impossible - in fact, it will take more force and effort.  It might hurt you and your shovel.
Similarly, in Deep Tissue, it makes sense to reduce tension and fascial adhesions in more superficial tissues first, making it easier to get to those deeper layers.
This gives the deeper tissues space to relax into and creates longer lasting results.  
A Deep Tissue massage is also kind of like an Easter egg hunt - a bit of an unpredictable search for clues in the tissues.
When to get a Deep Tissue massage: When you have pain from muscle tension and knots, when you do repetitive movements that cause strain injuries, when you stay in static positions for long periods of time each day.