Generally there are two types of errors in an experiment, random errors and systematic errors. In this case there is a random error due to your limited ability to record the time of fall precisely. There may or may not be a systematic error due to the fact the electromagnet does not release the ball the instant you press the switch.
Random errors show up in your measurements because they are random. That is, when you measure the same thing many times you get results that are scattered. We generally assume the errors follow a normal distribution, so then we can calculate a standard deviation $\sigma$, and the final standard error from doing $N$ measurements is $\sigma/N$.
Systematic errors are much harder to find because they can't (or at least can't easily) be spotted from a statistical analysis of your results. If your electromagnet took e.g. 0.1 seconds to release the ball after you pressed the switch you wouldn't easily be able to spot this. So as a general rule we do the best we can i.e. calculate the random error. That's why you are being told to take the average value of the time (and the standard deviation?). If there is a systematic error due to the magnet you would have to find that by other means. For example you could do the experiment for a range of different heights.