What is the literal interpretation for having a very low power (~30%)? I am going to be conducting an experiment where I have two discrete samples. I have a limited number of samples, and when I calculate the Power of the test, (given a set number of samples, and difference in the proportions that would be significant), it is low (~30%). 
I am not a statistics guru, but it seems to me this experiment isn't even worth running. What are the practical implications of having very low Power? I understand that Power is the probability that the test will reject the null hypothesis, given that the null hypothesis ought to be rejected, but I am still having a hard time wrapping my head around what this means. Is it equivalent to saying that any difference we see between the two samples is with the "noise" of the experiment?
 A: Perhaps an example will help with the understanding.  The following is some R code (I don't have easy access to Minitab and R is free):
n <- 100
one <- rbinom(10000, n, 0.45)
two <- rbinom(10000, n, 0.55)

out <- sapply(seq(along=one), function(i) prop.test( c(one[i],two[i]), c(n,n) )$p.value )

plot(one,two, asp=1, pch=16, 
  col=ifelse( out <= 0.05, '#ff000008','#00000008' ) )
abline(0,1, col='blue')

The first 3 lines generate 10,000 instances of 2 datasets (idependently) of size 100 (a little bigger than your sample size, but close enough), one where the probability of the event is 45% and the other with probability 55% (this represents the difference of 0.1 mentioned in the comments, you can easily rerun this for other values).
The next line goes through and calculates a p-value for each pair of numbers and the last few lines create the following graph:

Each point represents the possible results (number of successes in group 1 vs. number of successes in group 2), more opaque points represent multiple points on top of each other.  The blue line is $x=y$ where they are exactly equal and the red points are those with a significant p-value (<0.05).
So if you run an experiment with 2 samples of 100 each where the true probabilities are 45% and 55% then that will be the similar to randomly picking a point from this plot.
You can see that there are a lot more black/grey points than there are red points (the fact that about 30% of the points are red corresponds to the 30% power).  There are quite a few cases where you get the same number of successes in each group or more in group one than in group two.
So if you run this experiment there is a pretty good chance (about 70%) that you will not be able to tell the true difference (of 0.1) from random chance and will have wasted your time/money.  But you can rerun the simulation with different sample sizes and different effect sizes (and different exact probabilities, 0.05 and 0.15 give quite a different picture even though the difference is still 0.1) to see what the effect is and under which conditions it would be worth the effort/cost to run the experiment. 
A: As others have explained, the power of a test is the probability to reject the null hypothesis at the specified error level, for a given effect size and a given sample size (notice that those are the three things you need to provide to the software to run the power analysis – it's possible that the error level is implicitly assumed to be 5%).
One difficulty in this is the effect size. Sample size is easy to understand, error level is often constrained by tradition but choosing an effect size always involves a bit of guesswork. One approach is to take the smallest effect size that would matter in practice. This would guarantee that the study has a reasonable chance to detect any practically meaningful effect. You can also consider typical effect sizes in your field or area of research. You would run the risk of missing smaller yet practically meaningful effects but you would at least have a good chance to detect effects similar to those found in previous studies. The best is to play with the inputs and consider several scenarios.

it seems to me this experiment isn't even worth running

If the design cannot be adjusted at all and the effect really is that small and unlikely to be bigger, this seems like a defensible position and one that researchers should at least examine more often. That said, there are still many things you can do to increase power. Most obviously, you can increase the sample size. If that's too costly or not available, you can also try to increase the effect size (e.g. by using a stronger manipulation or a better measure).
Finally, if nothing else is possible, you should also consider increasing the error level. It might be difficult to defend if you want to publish the result in a peer-reviewed journal but there is no reason to rigidly follow the traditional thresholds (5% for type I error and 20% for type II error) if finding out any potential effect is more important to you than avoiding to falsely detect one.
