How did a centrally planned economy influence economic growth in the former Soviet Union?

This is a complicated question difficult to reduce to a short answer and depends on the time period.  But it's helpful to highlight some of the fundamentals of the former Soviet Union's centrally planned economy by viewing it through the lens of the collapse of the country in 1991.

The political climate, particularly the arms race of the 1980's, resulted in severe misallocation of resources by the central planners. Some economists estimate that more than 50% of the government budget in some years went towards production of arms, resulting in underinvestment in industrial goods needed for the rest of the economy. As a result of this underinvestment, shortages became more common and long lines of consumers looking for basic goods was frequent.

Central planning also resulted in low worker productivity. There were few incentives for workers to increase their productivity, a common critique of socialism/marxism. One Russian economist, investigating low productivity in Soviet mines, concluded that the workers had no incentives and

"The Soviet system is not working because the workers are not working"

In a very broad sense, the centrally planned economy resulted in economic growth that the government thought was most important: growth of the military-industrial complex. The result, as discussed in the first point above, was detrimental to other areas of the economy.