Interest on current accounts is usually given as an annual equivalent rate figure. This is like the APR figure you'll see on credit cards and is an indication of the interest you would receive if it were all paid at the same time, once a year. It provides an easy way to compare products from different banks.
Some high-interest accounts may have minimum requirements for monthly deposits, or penalties for withdrawals. If they suit your banking habits, they may still be good for you.
While interest rates can change, your bank should notify you when they do. Don't assume every glossy leaflet they send is junk mail - some of it may be important, so check before throwing it in the bin!