Equity is simply what you own minus what you owe. They are very valuable because they represent your worth -- what you can afford. There are three types of equity (beyond finance, though):
People Equity, and
Financial equity is the most known type. It is your assets minus liabilities. When you do a rough calculation of what all you own is worth (properties, cash and investments) and deduct from it what you owe, the result is your financial equity.
People equity is all about your network: the people you are in good terms with minus the people who will like to see you dead. Usually, you'll get people equity on your way to getting financial equity. That is the origin of the quote: "Your network is your networth." And when you've got a lot of financial equity, it becomes really hard to not have a very large people equity also. Just think about Donald Trump, how many of us can say the things he say and still have people wanting to publicly associate with us.
Sweat Equity is the least popular type. The best way to explain it is to use a village water need story I came across. Once upon a time, there was a village 10 miles from a stream. The villagers would walk the long distance to fetch water for their basic needs. Two people, James and John, decided to build a business to meet this need. James got big buckets and began fetching water in large quantities from the stream which after deducting a small part for his own home use, he sells the rest. Over time he became stronger and better at fetching water from the stream and was immediately making cool money. John, however, decided to dig a canal from the stream to the village. He spent 10 months with no pay digging the canal. Then when he was done, he could sell the water cheaply to the villagers and put James out of business. He became a millionaire. And that's how powerful sweat equity is. It is more than just sweating, but about doing what no one wants to do because it's very difficult. Carrying bucket is not difficult, or doing whatever gives immediate result. It is doing what will not give you result for a long time with hard work that refers to greater sweat equity.