The verbs être and avoir are called auxiliaries - the verbs which are devoid of their meaning and which, associated with the past participle, serve to form the compound tenses.
Some verbs can be conjugated with the auxiliary avoir as well as the auxiliary être. When the conjugator has to conjugate one of these verbs, it proposes both forms. These are variants that are displayed in sequence in the conjugation table. It is however possible to choose which auxiliary to display by selecting variant1 or variant2 from the drop-down menu: Variants. Below is a non-exhaustive list of verbs used with the two auxiliaries avoir and être :
Semi-auxiliary verbs are verbs that are also devoid of their meaning and can be used together with another infinitive to add a nuance of tense or aspect. Thus aller + infinitive is used to express the near future, se mettre à + infinitive is used to mark the starting point of the action.
To learn more about French auxiliaries, visit the French Grammar Online website.