The biggest change is Twitter will now hold on to users data for 30 days, up from 10. This data is gathered as the user visits websites with embedded tweet or Twitter share buttons. The company claims the data is never matched up to a person's name, email address, phone number, or Twitter handle. After 30 days the data will be deleted, obfuscated or aggregated.
Twitter has altered how it shares non-personal, aggregated and non-device level data that under select partnership agreements, AKA advertisers, that will allow it to be linked to your name, email, or other personal information if you give the partner your consent.
To personalize a user's experience across multiple devices the app will now associate that browser or device with your account for purposes such as authentication and personalization. This will allow Twitter to, for example, bring in content on sports across all a person's devices, if that individual visited a sports-themed site via that browser.