the sentence answers itself really - but in essence and as simply as possible- interest, while representing the "cost" of funds - also represents the expected return on a domestic investment.
so when domestic interest rates are lowered - capital flows out of that country in an effort to seek higher returns elsewhere - as a result of this capital flow there is sellside pressure on the domestic currency ( in favor of a higher yielding currency ) as investors exit their positions.
You would rather invest your money in a currency that offers a higher interest rate (return) than one that offers a lower interest rate. For example, if US interest rates rise, more foreigners will pour money into the U.S. This would increase demand for the USD and lead to an appreciation in the dollar.