There are a number of different marketing tactics for food.
Organic meets USDA organic standards. You may or may not agree completely with what makes organic standards (I'd rather have grass fed non-organic beef than industrial organic beef. There are a lot of great small farms out there that don't qualify as organic, but have better farming practices than large scale organic farms.)
Natural does not meet USDA organic standards. It has no laws around marketing your food as natural, so read the packaging carefully - but is generally used for something that can't be labeled organic but meets some of the requirements - i.e. no hormones or no GMOs.
Industrial organic is large scale organic farming and manufacturing. There are large scale "natural" foods as well. If you are concerned about the life your chicken lead before it ended up on your plate, industrial organic chickens don't have it much better (and in some ways worse), than your normal grocery store chicken.
Local means that it was sourced within a reasonable distance (100 miles or so). Usually local means small farmers, but not always.
Is it worth the money? Organic MAY or MAY NOT be healthier for you - there isn't a lot of data, but some people think its a common sense thing that eating pesticides is bad for you. Or preservatives, or what have you. The jury is out. Organic MAY or MAY NOT taste better for you.
We eat the majority of our food in some form of smaller scale, local, natural, and/or organic. But, sometimes, a person just wants a McDonald's hamburger, even if it barely counts as food.