The object of a clause is the noun which is having the verb done to it. Depending on which action is taking place, you can have both or either a direct (accusative) object or an indirect (dative) object in a clause.
‘Direct object’ is just the fancy terminology grammologists use to describe the object which is the target of a normal, bog-standard verb which puts it in the accusative case. For example, the underlined objects in these sentences are direct objects:
Ich habe meinen Lehrer gefragt, ob ich nach Hause gehen darf.
Suzi futtert ihre Katze.
Jungs, macht eure Hausaufgaben SOFORT!
‘Indirect object’ is the other schminky-pinky word which is used to describe an object which is the target of a verb or construction which puts it in the dative case. Click here for the full lesson on the dative case and the indirect object. Here, the underlined objects are indirect objects:
Der Arzt gibt meinem Vater seine Visitenkarte.
Schick mir bitte die Unterlagen.
Sie hilft den Mitarbeitern, Stress zu vermeiden.
Note that in these sentences we also have direct objects: ‘seine Visitenkarte’, ‘die Unterlagen’ und ‘Stress’. You don’t always have to have one of each type of object in a clause, but it does happen often, so it’s important to get your cases right to make it clear who in the sentence is doing what.