This is a typical circuit. Touch & goes are usually accomplished over the runway portion, although you can also do a full stop landing and taxi back to the end to depart and go around again. They are usually flown around 1000 feet AGL, although some airports may have specialized policies. Circuits can either be left turns (like this one), or right turns, depending on the specific airport's regulations and/or ATC desires.
A circuit doesn't form a rectangle around the field, rather one edge of the rectangle is the runway. It indeed can be used to practice turns and maintaining altitude, with the main focus being on demonstrating reciprocal headings, situational awareness, and general thinking ahead of the aircraft, along with landing practice.

Another pointer: generally speaking, with light aircraft in particular, this pattern should be flown so that on the downwind leg, you are about 1/2 mile from the runway horizontally, and your base leg should be about a mile from the end of the runway (or whatever your desired touchdown point is). It's not a rule really, more just a good formula for most smaller, slower airplanes.
The idea is that once you are that low (pattern altitude), you want to be able to  glide to the runway if the engine quits.  If your downwind is 3 miles away from the runway, that won't be possible. Half a mile works pretty well in most cases. 

Now, if you are entering downwind at a 45-degree angle, you should be at pattern altitude farther out, to avoid descending on top of someone else doing the same thing... this makes you a bit vulnerable if the engine quits, so it is best to start this entry- or any other kind of entry- no more than 3 miles out. At this point you'll be flying a little faster than in the pattern, so you won't be in that vulnerable position very long.

With faster and larger ships, flying a higher 1500-ft. AGL pattern, the distances are usually doubled, for the same reason.

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Maybe it's just me but I sense a little 'tongue in cheek' here.  Nice traffic pattern graphic.

Sir Puma wrote on Dec 2^nd, 2009 at 10:35pm:
Perhaps I see humor where none was intended.  At the start, touch and go's are a means of accomplishing a landing and a takeoff in one pass.  Ideally each should be a complete landing to a slow roll followed by a takeoff with everything appropriately set.  Some airports are too busy to allow more than an immediate transition from on to off.  When you're comfortable with your landing skills, it's good to pick a spot and see how close you can 'touch' - ideally in the first third of the runway so there's always room for the 'go'. 

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Back in my salad days at one busy VFR airport, thats what pattern practice became from time to time as we launched backed up departures.  Often had eight to ten doing a half hour or so of four medium banked turns 'about an airport'.  This was shortly after Vietnam and the air was full of guys spending their GI bill - spent a few myself.  .