eilen
to hurry
To move or travel quickly because one is in a hurry; to rush or hasten.
Ich muss jetzt nach Hause eilen, weil ich noch einen Termin habe.
I have to hurry home now because I still have an appointment.

to hurry
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to hurry
To move or travel quickly because one is in a hurry; to rush or hasten.
Ich muss jetzt nach Hause eilen, weil ich noch einen Termin habe.
I have to hurry home now because I still have an appointment.

The verb 'eilen' (to hurry) belongs to the word family around 'die Eile' (haste), which means 'great haste' or 'urgency'. So someone who 'eilt' (hurries) is 'in Eile' (in a hurry).
In großer Eile rannte er zum Bahnhof.
In a great hurry, he ran to the train station.
If a person or vehicle is the subject, 'eilen' (to hurry) means to move quickly. If 'es' is the subject, it usually means that something is urgent.
Die Sanitäter eilten zum Unfallort.
The paramedics hurried to the scene of the accident.
When 'eilen' (to hurry) describes movement toward a destination, the perfect tense is formed with the auxiliary verb 'sein'. Without a clear destination, 'haben' is also possible, but less common.
Er ist nach der Arbeit direkt nach Hause geeilt.
After work, he hurried straight home.
The impersonal form 'es eilt' (it's urgent) is a very common fixed expression. It is used to express that a situation is urgent and requires quick action.
Schick mir die Dokumente so schnell wie möglich, es eilt wirklich sehr.
Send me the documents as quickly as possible; it's really very urgent.
to run
'rennen' and 'eilen' can both mean that someone wants to get somewhere quickly. However, 'rennen' describes the physical movement more strongly: you are really running very fast. 'eilen' emphasizes more that you are in a hurry; you might walk quickly, drive, or generally hurry up. Also, people often say 'Es eilt' (it's urgent) when something is urgent. Learners confuse the words because both have to do with time pressure. As a guide: if someone is moving quickly on foot, 'rennen' fits. If the urgency is more important, 'eilen' fits better.

Der Arzt eilt zum nächsten Patienten, weil der Fall dringend ist.
The doctor hurries to the next patient because the case is urgent.
Nach dem Klingeln rannte Max schnell zum Bahnsteig.
After the bell rang, Max quickly ran to the platform.