sich entschuldigen
to apologize
To ask for forgiveness for a mistake, an inconvenience, or rude behavior.
Ich möchte mich für meine späte Antwort entschuldigen.
I would like to apologize for my late reply.

to apologize / excuse
Loading your saved state.
to apologize
To ask for forgiveness for a mistake, an inconvenience, or rude behavior.
Ich möchte mich für meine späte Antwort entschuldigen.
I would like to apologize for my late reply.

The verb is made up of 'ent-' and 'Schuld' (guilt/fault). The prefix 'ent-' often means 'to take away' or 'to remove.' So 'entschuldigen' (to apologize/excuse) literally means to take the guilt or blame away from someone.
Kannst du mein Fehlen bei der Sitzung bitte entschuldigen?
Can you please excuse my absence from the meeting?
The meaning changes depending on the object: 'sich entschuldigen' (reflexive) means to ask for forgiveness. 'Jemanden entschuldigen' (accusative object: person) means to justify an absence. 'Etwas entschuldigen' (accusative object: thing) means to justify a mistake.
Er entschuldigt sich für sein Verhalten.
He apologizes for his behavior.
When apologizing for something, you use the preposition 'für' followed by the accusative. To apologize to a person, use 'bei' with the dative.
Ich entschuldige mich für die Verspätung.
I apologize for the delay.
The imperative form 'Entschuldigen Sie' (Excuse me; formal) or 'Entschuldige' (Excuse me/Sorry; informal) is a fixed expression. It is used to politely ask a question, interrupt someone, or apologize for something small.
Entschuldigen Sie, ist dieser Platz noch frei?
Excuse me, is this seat still free?
to explain / declare
'erklären' and 'entschuldigen' can both have to do with reasons. You use 'erklären' when you make something understandable, for example a rule, a problem, or a situation. You use 'entschuldigen' when it is about a mistake, a disturbance, an absence, or a polite request. Learners confuse the words because sometimes you explain a mistake and apologize at the same time. The difference is: when explaining, the goal is for someone to understand something. When apologizing or excusing something, you ask for forgiveness or make clear why something is not so bad.

Im Büro entschuldigt sich Tom, weil er zu spät zum Frühstück kommt.
At the office, Tom apologizes because he is late for breakfast.
Die Lehrerin erklärt den Kindern, warum gesundes Essen wichtig ist.
The teacher explains to the children why healthy food is important.