Covered interest parity is the idea that exchange rates will adjust to equalize interest rates between two countries, using the forward exchange rate to convert the future returns in each country.
For example, suppose you wanted to deposit $100 in an interest-bearing account for three months. In the US, the return on that account would be $100(1 + i US), where i US is the three-month interest rate in the US. Alternatively, you could deposit the $100 in the UK. To do so, you would convert the $100 to GBP at the current exchange rate, Spot, valued in GBP/$. The return after three months would be $100 Spot (1 + r UK). To convert this return back to dollars, use the forward rate, Forward, denominated in GBP/$: $100*Spot(1 + r UK)/Forward. The two strategies should produce the same return:
$100(1 + i US) = $100*ef(1 + r UK)/es
or, 
Using a bit of algebra, we can convert this equation into i UK - i US = Forward premium. The forward premium is measured as a percentage; 1% means that the forward exchange rate is 1% higher than the current spot rate. Since the exchange rates are measured as GBP/$, the forward rate implies an appreciation of 1% in the dollar.
If the UK interest rate is currently 7% and the US interest rate is currently 4%, CIP implies that the forward premium should be 3%. That is, the forward value of the dollar is 3% higher than the spot value of the dollar. The dollar is expected to appreciate by 3% over the length of the term of the deposit.
If the Bank of England raises interest rates, the forward premium will rise and the dollar will be expected to appreciate.