
hinterher
afterwards
After that in time; at a later point.
Wir gehen jetzt ins Kino und könnten hinterher noch etwas essen gehen.
We're going to the cinema now and could go for something to eat afterwards.
afterwards / behind
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afterwards
After that in time; at a later point.
Wir gehen jetzt ins Kino und könnten hinterher noch etwas essen gehen.
We're going to the cinema now and could go for something to eat afterwards.

behind
Following spatially; behind someone or something.
Der kleine Hund lief seiner Mutter überall hinterher.
The little dog ran behind his mother everywhere.

to be behind
To be behind in a development or with a task; to be unable to keep up.
Nach seiner Krankheit war er im Unterrichtsstoff ziemlich hinterher.
After his illness, he was quite behind in the course material.
The adverb is made up of 'hinter' (behind) and 'her' (movement toward the speaker). This structure illustrates the basic meaning of following, whether spatially or in time.
Lauf nicht so schnell, ich komme ja kaum hinterher!
Don't run so fast; I can hardly keep up!
As an adverb, 'hinterher' can stand in different positions in the sentence. If it is in position 1, the verb follows directly after it (inversion). It can also stand in the middle of the sentence.
Hinterher haben wir alles verstanden.
Afterwards, we understood everything.
The expression 'hinterher sein' means to be behind. It is often completed with the preposition 'mit' and the dative to indicate what someone is behind with.
Ich bin mit meiner Arbeit total hinterher.
I'm totally behind with my work.
The spatial meaning ('hinterdrein', behind/after someone) is usually used with verbs of movement such as 'laufen' (to run/walk) or 'fahren' (to drive/go). The temporal meaning ('danach', afterwards) refers to the sequence of actions or events.
Erst die Arbeit, hinterher das Vergnügen.
First work, then pleasure afterwards.
behind
When describing movement, hinter and hinterher can both indicate that someone is farther forward. Hinter names the spatial position with a complement, while hinterher expresses that someone is following another person. Use hinter for the position and hinterher for following.

Die Tochter geht ihrer Mutter durch den Bahnhof hinterher.
The daughter follows her mother through the train station.
Die Tochter geht hinter ihrer Mutter durch den Bahnhof.
The daughter walks behind her mother through the train station.