Sweepstakes often use passwords to make it easier for you to return and enter on a daily, weekly, or monthly basis, depending on their entry frequency. If you create a log-in with a username (or your email address) and password, you don't have to enter all of your information each time you want to enter.
This does not, however, mean that you should be using the same password to enter sweepstakes as you use for other websites. These sweepstakes are not asking for your email password or your banking password! They are asking you to create a new password for your sweepstakes entries.
The safest practice is to create a new password for each sweepstakes you enter, but it's critical that you don't re-use a password that you use for any critical purpose, including your email accounts, your bank or credit card accounts, your Facebook and Twitter accounts, etc.
Practicing safe password management will protect you if you accidentally enter a scam sweepstakes, or if a legitimate sweepstakes database is hacked. (For an example, see Hackers Publish Sweepstakes Database Online.)
See How to Choose a Sweepstakes Password for tips on how to manage multiple passwords across multiple accounts.