Your 20minute "lay of the land" presentation should address the following
points:
1. What is the problem?

Examples

Definition (inputoutput)

What would solution look like?
(Eg, "any X s.t. Y", or "an X s.t. Y which
maximizes Z", or ..)
2. Why is the problem important? (ie, why should I
care?)
Ie, if it was solved...

what would that make possible?

would the world be a happier place?

would I make a gazillion dollars?
3. Why isn't this task trivial?
(Ie, explain why I can't just solve it in my
sleep...)
Here, it may be useful to point to

theoretical results (eg, "task is NPhard")
... coupled with an argument for why the specific tasks
that people address,
will be large, and be difficult (ie, not a special
case).

mention realworld situation
(eg, "dozens of PhDs in CompanyX are working
full time on this...")

present a wellchosen example to give some insights on the
complexities here
 an example is one that is easy to state, but not obvious how to solve.
(Eg, show that obvious solutions don't work)
4. The people (researchers, developers,
technicians) who really need to solve this
problem: What do they do?
This should be a quick survey of the TYPES
of techniques

do companies/people really commit the resources to find the
exact solutions to general, hard problems?

are there special cases where exact solutions are possible?

are there good approximations?

are there usuallyeffective probabilistic/stochastic algorithms?

...
(Part 4 is the "lay of the land" portion; this should
be the bulk of the presentation  say 15 minutes.)
Your final presentation  during the last week of the
course  should quickly summarize 14, then spend most of the time
giving the actual results.
Some other comments, about presentations in general:

People are uniprocessors: if they are reading, they are NOT listening.
Therefore, it makes sense to write as LITTLE material on your slides
as possible.
 Avoid complete sentences; use Bullets!
 Use LARGE fonts

Give a simple examples FIRST, before giving the formal definitions, theorems,
etc.
Then perhaps use that example to "instantiate" the definitions, etc.
(Don't worry: people typically do an amazingly great job of generalizing
from such examples.)

Try to avoid technical terms, if at all possible. (Or at least give
a simple example of the idea.)