Gesinnungsethik is basically a caricature of Kantian deontological ethics or - which he puts on the same level - religious (here: Christian) fanatism or ethical absolutism. The line between Gesinnungsethik (ethics of conviction) and Verantwortungsethik (ethics of responsibility) are almost exactly corresponding to what is called deontological vs. utilitarian (rather: consequentialist) ethics in contemporary discourse.
Before introducing the definitions, he invokes reasons why politicians cannot possibly blindly follow ethical principles or values without regard for the reality of the world and men (page numbers by Politics as a vocation, in: The Vocation Lectures, Hackett, 2004):
The Sermon on the Mount (and
by this is meant the absolute ethics of the Gospel) is a far more serious business than is imagined by those who like to quote its com-
mandments nowadays. In truth, it is no laughing matter. We may say
of it what has been said about causality in science: it is no hansom
cab that can be stopped anywhere, to jump into or out of at will.
Rather, the sermon is a matter of all or nothing; that is the point of it if it is to amount to anything more than a set of platitudes. For example, consider the rich young man who "went away sorrowful: for he was one that had great possessions. " The Gospel's commandment is unconditional and unambiguous: give up everything that thou hast - absolutely everything. The politician will say that socially this is a senseless demand as long as it does not apply to everyone. That means taxation, redistribution, confiscation-in a word, coercion and order applied to everyone. The ethical commandment, however,
ignores such matters entirely; that is its nature. (81-82)
To more clearly work out how this ties in with Kantian ethics:
Such a man believes that if an action performed out of pure conviction has evil consequences, then the responsibility must lie not with the agent but with the world, the stupidity of men-or the will of God who created them thus. With the ethics of responsibility, on the other hand, a man reckons with exactly those average human failings. As Fichte has justly pointed out, he has absolutely no right to assume human-
kind's goodness and perfection. He does not feel that he is in a position to shift the consequences of his actions, where they are foreseeable, onto others. He will say, "These consequences are to be ascribed to my actions." With an ethics of conviction, one feels
"responsible" only for ensuring that the flame of pure conviction, for example, the flame of protest against the injustice of the social order, should never be extinguished. (84, bolded mine)
This is a clear paraphrase of Kant:
[I]f you have by a lie prevented someone just now bent on murder from committing the deed, then you are legally-accountable for all the consequences that might arise from it. But if you have kept strictly to the truth, then public justice can hold nothing against you, whatever the unforeseen consequences might be. (On a supposed right to lie out of philanthropy, Cambridge 1996, 8:427)
To be truthful (honest) in all declarations is therefore a sacred command of reason prescribing unconditionally, one not to be restricted by any conveniences. (ibid)
In other words: According to Kant, you have to follow your sacred duty no matter what. And if you do, you should not be held accountable for any negative consequences arising out of your rightful, ethical behaviour, since they would arise out of the contingent circumstances outside of your own sphere of power of acting.
Now, what Weber does is putting any such deontological ethics under the name "Gesinnungsethik":
We need to be clear that all ethically oriented action can be guided by either of two fundamentally different, irredeemably incompatible maxims: it can be guided by an "ethics
of conviction" or an "ethics of responsibility." This does not mean that an ethics of conviction is identical with irresponsibility or an ethics of responsibility with a lack of conviction. Needless to say, there can be no question of that. But there is a profound abyss between acting in accordance with the maxim governing an ethics of conviction and acting in tune with an ethics of responsibility. In the former case this means, to put it in religious terms: "A Christian does what is right and leaves the outcome to God" while in the latter you must answer for the (foreseeable) consequences of your actions. (83, bolded mine)
And, as we have already seen, he argues that this kind of ethics is impossible for the politician to follow (he has more similar arguments to offer). Here, he does again go against Kant's doctrines, who argued in his Towards Perpetual Freedom that the political maxim should be following the categorical imperative, ie. that good politicians are only they who follow his deontological ethics in the hope that other politicians will eventually do the same.
Here, Weber clearly has a more negative view and agrees with Fichte that humans simply are not that good and will take advantage of politicians if they act naively after principles only.
The problematic aspect of his turning against Kant here is that one of the major premises of Kant is that everyone should do the same, ie. most of his arguments against the commandments (which were formally - albeit never materially - criticised by Kant as well) just depend on his more negative image of the human nature, which led him to advocate for realpolitik.