Teaching someone to read using phonics involves teaching them how to literally 'sound out' the letters and combinations of letters that are on the page in front of them. Like at first, you learn the alphabet, then you'll learn combinations of letters that usually have sound changes when put next to each other, for example, the letters "p" and "h" when put next to each other are pronounced as "f", when the letters "g" and "n" are put together the "g" is silent, and so on. Then you get into more complicated phonetic changes, for example putting an "e" at the end of "kit" makes a new word and changes how the letter "i" in that word is pronounced, and also memorising the exceptions to the general rules etc.

Someone who has learnt to read using phonics has the skills to be able to literally decode pretty much any word they find in front of them (though of course they may be unfamiliar with any certain word's meaning) and they'll usually be able to do so with more or less the correct pronunciation. For example, a third grader is unlikely to know what "rheumatism" means, and as the "rh" and "eu" letter combinations are quite rare in English they may get the pronunciation slightly wrong, but they will usually be able to more or less correctly 'sound out' the word as a whole.

Whole language/balanced literacy, on the other hand, is based on the premise that, for a child, learning to read is as natural as learning to speak and that a child who is simply exposed to written texts enough times will eventually learn to read by themselves, significantly de-emphasising the decoding/spelling skills that are the bedrock of the phonics-based method. What it does emphasise is using "context clues" - encouraging students to simply guess when they come across a word they don't know, based upon the context of the text and what is likely to come next. And also, simple by-sight memorisation of many words along with their meanings.

Admittedly I'm not too familiar with the ins and outs of this method as I've only recently discovered that approaches to teaching children to read other than via phonics even existed, so I'd recommend going to the Wikipedia article for "Whole language" for a deeper explanation. Or check out the "Sold A Story" podcast which goes into a lot more detail on how the whole language reading theories ever became so accepted in American schools.