President Dwight Eisenhower is considered today to be a liberal Republican because he was not as dedicated to the idea of small government as modern Republicans are. He was also fairly pro-civil rights, as can be seen by his actions during the Little Rock crisis in the late '50s.
Today, Republicans are known for their desire to make deep cuts in government spending. This can be seen in the current debate between Democrats and Republicans over the budget. Eisenhower was not interested in making these kinds of cuts, however. For example, Eisenhower was the one who had the federal government create the huge interstate highway system. He also pushed for legislation that increased the number of people who qualified for Social security and he increased the level of benefits. He allowed the minimum wage to increase and he (unthinkable for a Republican today) thought the government should provide health insurance for people.
All of these attitudes would be out of place in today's more conservative Republican Party and so we characterize Eisenhower as a liberal Republican.