"He had offered me a beer."
Translation:Il m'avait proposé une bière.
Some verbs require agreement not with the subject of the sentence, but with the direct object. The majority of French verbs are conjugated with avoir in the compound tenses and do not agree with their subjects. However, avoir verbs require agreement with their direct objects or direct object pronouns when these precede the verb. (There is no agreement when the direct object follows the verb or with an indirect object.)
In the given sentence, Il is the subject ("who offers?" "he offers"). Note that the direct object, une bière follows the verb, therefore no agreement is required.
Une bière ? Il me l'avait proposée. Here la refers to une bière and, in this sentence, precedes the verb so requires agreement.
The speaker is telling someone about something that had happened (prior to some other past action). Since it refers to a previous past action, the pluperfect is used, i.e., he had offered, not "he has offered". Otherwise, the pluperfect works just like Passé composé, except that it uses the imperfect conjugation of the auxiliary verb. Does that help?