EV is obviously a huge thing and pretty difficult to understand. I'll try to give a very basic explanation, to accompany the article provided earlier. I'll try to avoid all the complicated math. I won't claim I'm an expert, but I think this should give you somewhat of an idea of how and why EV is important.

Basically, poker is a game involving a lot of randomness; every card you get dealt is random, every card your oponents get dealt is random, every community card is random. Then there's multiple ways a hand can be played (you can call a raise preflop with AK or you can 3bet, for example), so player actions can be random as well.

With that out of the way, whenever you want to calculate the profitability of a move, you have to take into account every variable, e.g. everything where randomness is involved. That sounds ridiculously complicated. And I'm not going to lie... It is!

But starting very simple, you know a move is profitable when it is +EV. The expected value of a move is simply the money you expect to make with that given move. So if you expect to win $10 by going all in with your AA, that move is +EV. If you expect to lose $10 by going all in with your 32o, that move is -EV. But I think you already grasped that.

The reason you really need to know so much about EV, is because it's the single most defining element in poker; absolutely everything revolves around EV. If a move is not +EV, you shouldn't make it (there are expections to this, beware), because you expect to lose money in the long run. And you obviously don't want to be losing money. And this goes back to the whole element of randomness in the game of poker; you may lose money once by making a +EV move, but in the long run you'll be making a profit.

Obviously calculating your EV while playing is almost impossible, but that's not important. You can calculate EV when analysing your play. If you analyse your play and you're just looking at your hand and say "well, I think I might not have played this correctly, I think", you're doing it wrong. When you make an in-depth EV calculation, you can provide yourself with a sound, correct explanation of why your move was correct or not, and can also use EV to figure out the optimal move if your move was sub-optimal.

Now I'm not going to go in-depth on the calculation of EV, I think the article suggested above explains that fairly well. Also, I can recommend the series on "Putting EV to use" by Collin Moshman, even though it is specifically geared towards tournaments, the concepts apply to any form of poker.

http://www.pokerstrategy.com/video/#searchtext=putting%20ev%20to%20use&key=all&contenttype=0&gametype=0&tablesize=0&languages=en&levels=basic,bronze,silver,gold,platinum,diamond&lowerlimit=0&upperlimit=100&ob=date&od=desc&page=1&rpp=10
Now onto equity!

Equity is actually a very simple concept, and a very important one in the calculation of your EV. Equity is basically the percentage of the pot you own. So if you have AA against your opponent's 44, you'll have roughly 80% equity. That means that if you get it all in, you're going to win 80% of the time, and lose 20% of the time. Once you know this, you already have a foundation for the EV calculation. It's quite simple, really!

Here's a simple formula for you, which we'll put to use.

Equity needed to call = amount to call / (pot + amount to call)

So say you have JJ, your opponent goes all in pre flop, and you want to know if you can call. Lets assume the pot is 1000 and you have to call 600. That means that in order to call profitably, you need 600 / (1000 + 600) = 0.375 = 37.5% equity.

Now you have to give your opponent a range. Let's say we assume he shoved only AA, KK, QQ and AK. Comparing our JJ to a range of just QQ+, AK (using an app like Equilab), we see that we have 36.19% equity. Since we need 37.5% equity, we will have to fold out JJ to his shove. But what if we suspect villain is shoving wider, say TT+, AK instead? In that case, we have 43.23% equity, and we have a snap call.

That's how you can use equity to make decisions while you're playing. Of course this requires you to know a bit about how much equity your hand will have against specifc hand ranges. The article mentioned above also features a handy little table with a few of these comparisons, which I can definitely recommend memorizing. It's very useful to know that when you have pair over pair, you have 80% equity, and if you have a pair vs overcards, that it's roughly a coin flip. Knowing little things like these can help you make decisions more easily and more quickly.

I will end my wall of text here. Hopefully this was useful!