I’ll go line by line. My words will be in red, theirs in black:
“The theory that all knowledge derives from the senses, and that the data will speak for themselves without the benefit of any explicit theoretical perspective. (Basically here they mean that everything we know we have to have touched, seen, tasted, heard, or smelled. That’s the only way we can learn about stuff. Note:I don’t think this is a good definition, but that’s what it is in layman’s terms.) In the traditional view of empiricism it is believed that the mind of the observer plays no role whatsoever in forming knowledge, and that it somehow comes about as more and more ‘facts’ are discovered. (Basically, according to empiricism it’s not really you making your mind think. Instead, it’s just that all the stuff you see, taste, etc. comes together and creates thoughts and forms knowledge) Following the work of Kant and others, this view was modified to allow some role to be given to the mind in forming knowledge, though the problem has always been how to relate the two adequately. (The 18th-century German philosopher Kant basically said that it’s really the mind that does a lot of the work, and he put up a lot of convincing arguments to say that the mind plays a big part in our knowledge. So empiricists had to change their views to be more in line with this.) In positivism (Positivism is the idea that the best way to learn anything is through science.) this is solved by inductivism: the idea of the ability to infer general knowledge from particular sensory data. (Basically, inductivism says that your senses helps you see the things, and then your mind picks up on patterns or draws conclusions from this. For instance, I sense that every time I breathe air comes out of my nostrils, then I draw the conclusion that every time I breath I’m taking in air. This is induction.)Empiricism of various forms is the dominant epistemology in archaeology(Epistemology just means sort of “the way you find truth and knowledge”. So empiricism is the best way to find truth about archaeology); empirical data, achieved mainly through controlled observation, provide the basis of knowledge (We try to get different information from testing, watching, doing experiments.” and are generally kept separate from the distortions of subjectivity and any interpretations made (After we get the information, we try to figure stuff out from it, but make sure that there are no “subjective” illusions. For instance, if you put a stick in water it looks like the stick actually bends. But this is just subjective. With this scientific method we try to make sure we don’t get tricked like this)"
Hope that helps a little.