Standard deviation is a measure of dispersion within your data set whereas standard error is considered the level of error (dispersion) of your data from a population mean. Bigger sample sizes are likely to have smaller error - this makes sense if you consider the formula for standard error, which uses square root of N for the denominator...
I think I am right about this (I hope so, and hope that helps!)
The SD is a measure of the dispersion of the data around the mean.
If you have a sample (let us call it "sample 1") and you take some measurement on it (e.g. you take into account the heart's beats per minutes of a sample of people), you will find that the mean is, let us say, 60 with a SD of 10. This tell you how much variation there is in your sample and, if your observations are normal distributed, you are in the position to know how many observations lie between, say, the mean and given number of SD.
If you draw other samples (sample 2,3,4,5,6 on so forth) you will have other mean values; sometimes they can be 60, sometimes 58, sometimes 62, and so on (everyone with its own SD).
If you collect all this mean values (that is, the mean of sample 1, the mean of sample 2, the one of sample 3,4,5, 6, and so on) you will get a new distribution (called "sampling distribution") with a new mean and a "new" SD. This "new" SD (the SD of the sampling distribution) is the SE, that is a measure of the dispersion of the distribution of all those samples you have collected.
Usually, you are in the position to have just one sample, and you have to estimate the SE on the basis of the unique sample you have.
How do you calculate the SE? On the basis of the SD of your single sample (you can easily find the formula on the web).
The SE is important to calculate the confidence interval for the population mean. In other words, given your sample, you may want to infer the mean of the population the sample comes from. You get this by calculating a confidence interval in which the "true" population mean will lie, starting from the mean of your sample and from the SE that you estimated from the SD of your sample.
Hi, just to join the fray, I would say that the standard error is the standard deviation of an estimate ( most frequently the estimate of a mean, but it can be a regression coeficient or something else as well.)