I'll try to translate, with no guarantees:
The "Gesinnung" of a person is the entirety of moral, political or religious views and opinions the person holds.
"Gesinnungsethik" is an ethics where people make decisions based on these views they hold, i.e. based on what they identify as moral according to the values and principles they hold. In a narrower sense, Weber was talking about politicians or activists who act on the grounds of ideologies or religions that they follow. For them, simplified, an act is moral if it aligns with the ethics of their "Gesinnung".
Weber contrasts this with "Verantwortungsethik" (responsibility ethics), where decisions are made after also weighting in their direct consequences. To oversimplify, for Weber, a good politician might not always be able to just follow their "Gesinnung", however justified their views might be, but has to always stay "responsible" regarding the consequences of their acts, too.