Systemic errors are mistakes that are consistently made over time

Systemic errors are mistakes that are consistently made over time. If you have a balance that constantly reads everything as 0.1 grams heavier than it is, you've got a systemic error. While systemic errors may or may not be avoidable, identifying them helps you to figure out what's going on in your experiment.

Random errors are errors that just kind of happen without any pattern. If you do an experiment one day and make 4.5 grams of product, and then make 4.1 grams the next day and 3.8 grams the next, there's not really any pattern that suggests the same thing is going wrong in a consistent way. Random error is a lot harder to deal with than systemic errors, because you can't really compensate for something you don't understand and can't reproduce.

Of course, both sorts of errors are frequently human errors. Systemic errors may happen if you screwed up and did your experiment in a very humid environment, and random errors may happen if you have shaky hands and spill stuff a lot. If you're making either random or systemic errors, always assume that you're the source and act accordingly.