What is standard error used for? I'm using a tutorial I found and plotting mean values along with the standard errors to show my data. But I'm having a problem discussing the results. My plot is as shown below: some of the standard errors (shown as a error bar) vary much and some of them are very close to zero.

 A: As mbq says, error bars are a way of letting your readers to get a feel if the differences between two groups are significant - i.e. if the variation within each of your groups is small enough to believe that the difference you've found for the mean between your groups. 
All else being equal, larger error bars mean more within-group difference, but it looks like the y-axis of your plot is log-transformed, so the lower groups aren't quite on the same scale as the higher ones.
You should be aware, many of your readers won't understand what error bars represent, even if you explicitly explain it! Often you can achieve the same goal with a jittered dot-plot or a boxplot (or both together) to achieve the same effect.
A: Plenty of researchers have trouble interpreting these graphs. See http://scienceblogs.com/cognitivedaily/2008/07/31/most-researchers-dont-understa-1/ for a more detailed elaboration.
A: In general, the standard error tells you how uncertain you are that true value of the top of the bar is where the bar says it is.  When there are multiple bars, it can also enable comparisons between bars, in the sense of a statistical test.  However, interpreting them in this way requires some assumptions, shown graphically below.  If you are really interested in comparing the bars to see if the differences are statistically significant, then you should run tests on the data and display which tests were significant,like this.

In addition, I would suggest using confidence intervals rather than standard errors.
This paper is well worth the read:
Cumming and Finch. "Inference by Eye: Confidence Intervals and How to Read Pictures of Data." Am Psych. Vol. 60, No. 2, 170–180.
Their overall conclusion is: "Seek bars that relate directly to effects of interest, be sensitive to experimental design, and interpret the intervals."
For independent samples, using confidence intervals, half overlap of the CIs means the difference is statistically significant.

For independent samples using standard error bars instead, the following graph shows you how to figure out statistical significance:

A: Error bars in general are to convince the plot reader that the differences she/he sees on the plot are statistically significant. In an approximation, you may imagine a small gaussian which $\pm1\sigma$ range is shown as this error bar -- "visual integration" of a product of two such gaussians is more-less a chance that the two values are really equal.
In this particular case, one can see that both the difference between red and violet bar as well as gray and green ones are not too significant.
