House price stability is a measure of how much house prices are changing in a given area over a given time. If house prices are level or going up this is seen as a good time to be investing in property and all else being equal banks will tend to lend more in mortgages as there is less danger of falling house prices and negative equity.
Conversely, an unstable or falling housing market is a risky time to invest in the housing market and banks will tend to hedge their bets by not lending so much on mortgages. The problem is that these trends are very hard to predict and no-one really knows how the market is behaving except in hindsight. There is a certain interdependence between house prices and the Bank of England Base Rate , as this has knock-on effects onto the money markets and therefore into mortgage interest rates. Higher interest rates mean people are more likely to save and less likely to borrow, and mortgages and other forms of borrowing become more expensive. A word of caution also: as mortgages are a large form of borrowing and the market can change at any time it is very important to talk any mortgage or re-mortgage decisions through with an expert from your bank or building society.
N.b. Individual circumstances vary and these articles only provided for illustrative purposes. I recommend you see a bank assistant or a financial advisor if you need help with your finances.