Well, would you drink a glass of pesticide? I'm guessing no. So you want to avoid eating pesticides on your food, and eating organic is the best way to do it. Remember, just like plants absorb nutrients from the water and soil, they absorb toxins - so you can't just wash them away.
But organic is more than just food that's grown without pesticides. it also means no chemical fertilizers, sewage sludge, radiation or genetically modified organisms. So if you're concerned about food irradiation, or GMOs, then buying organic means you're automatically avoiding them. Organic food is cleaner, and more naked than conventionally-grown produce. It's been shown to contain more anti-oxidants and micro-nutrients than non-organic produce, so it's healthier for you too.
Since organic produce is more expensive, some people choose to buy organic versions of only the most toxic items. These fruits and vegetables absorb chemicals and pesticides more than others, and often have edible skins. Remember how you mom used to say that the skin contains all the vitamins and nutrients? She was right. But pesticides also like to hang out there. There are annual dirty dozen lists you can refer to, but don't forget that these lists don't only apply to fresh produce. If you decide to stop buying conventional tomatoes and hot peppers (two usual offenders), then think about the other products you buy, like salsa and pasta sauce that contain those items.
There are also yearly lists of conventionally-grown foods that are safe to eat, usually because we don't eat the parts where all the absorbed pesticides congregate, or bugs just aren't that into them, making pesticides unnecessary. But if you can afford the extra cost, buying all organic products lets you do something to promote your favorite causes just by shopping for dinner. Buying organic keeps toxic chemicals out of the soil and water supply, so it's an easy way to help the environment - you were going to the market anyway. Also, since organic farming requires less resources than conventional farming, buying organic can help fight global climate change. Care about social justice? Daily exposure to chemical fertilizers causes health problems for farm workers, so buying organic keeps your money from paying for that.
People often think that organic fruits and vegetables don't taste any different from conventionally-grown. But that's usually before they've actually tasted fresh, organic food. Ever had organic celery? It has a flavor. That watery, bland cliche diet food is full of taste when it's grown organically. Maybe it's all the micro-nutrients absorbed from top-soil that hasn't been depleted by harsh chemical fertilizers. The difference is startling because conventional celery doesn't really taste like anything. And remember tomatoes that taste like tomatoes? Fresh off the vine, really ripe, and not some poor excuse for a tomato that lurks in the supermarket in the depth of winter. Organic tomatoes taste like real tomatoes.
So if your kids aren't enthusiastic about eating their veggies, give them organic. They'll turn into mini-food snobs, but they'll get all their vitamins and nutrients from their food instead of a chewable tablet.
If you care about your health, the environment, or how great your food tastes, then organic really is that important.