The simple act of transferring the balance from one credit card to another does not necessarily have two hurt your credit score. However, they may be an initial negative impact on your credit score as transferring the balance will add a new enquiry to your credit report. If you are getting a new credit card with a lower rate of interest to transfer the balance to it will decrease your debt utilization ratio. Debt utilization ratio is the amount of total credit that is available to you compared to the the actual amount that you utilize. As long as you do not incur further debt on your credit cards getting a new credit card with a lower rate of interest will increase your credit limit while the balance will remain the same. This will have a beneficial effect on your credit score in the long run as a loaded utilization ratio is considered to be the sign of responsible management of credit.
As it happens with any kind of change in your credit history the initial impact on your credit score may be temporarily negative. It may take some time for positive information such as repayment of the transferred balance on a regular basis to have the desired effect on your credit score. Also, as you were most likely going to transfer the balance on a card that has a lower rate of interest you will end up paying your debts faster. As more of the payment you make will go towards paying off the principal amount rather than the interest your balance on the credit card will produce faster. As the balance reduces your debt utilization ratio will reduce even further having a positive effect on your credit score.
The important thing to keep in mind is to not use any of the credit cards for further credit till the time that you have a paid off the entire balance. It may be tempting to use the credit cards from which you have transferred the balance has now they will have a zero balance and the entire credit limit available to use. But using these cards again will not only increase your debt utilization ratio but you further on the debt which might negate the advantages of transferring the balance on low-interest credit card and have you back under the same difficult situation where you face and manageable credit card debt.