If a stock has a beta of 0.7 that means for every percentage gain, the broad market makes, this particular stock will make a 0.7% gain. So if the market moves 10% up, this stock will move up by 7%.
You can define Beta as a value that shows the correlation between the price movement of a major market index and the price movement of a particular stock. A beta of 1 shows that there is a perfect correlation between the index and the stock, effectively if the market goes up by 10% then the stock will also go up by 10%.
Because large companies also form a large part of any major index, the Beta of large companies is always close to 1. In any market movement it is the smaller companies that go up or down substantially and therefore the beta of smaller companies is generally much higher than 1. This means that a 10% gain in market leads to a more than 10% gain in such stocks.
Hardly any stocks have a negative beta because that means that when the market moves up, this stock goes down and vice-versa and this is rarely ever the case with any stock.
A beta of zero indicates that there exists no correlation between how the stock moves and how the market moves and it is rare to find such stocks also.
Beta is calculated using regression analysis and is a measure of stock volatility. Ultimately what we are saying looking at a Beta value is how much the stock is expected to rise or fall with respect to the rest of the market and this is nothing but a means to express volatility.