schließlich
finally
At the end of a process or development, or after a long wait; at last.
Nach stundenlanger Diskussion haben wir uns schließlich auf einen Kompromiss geeinigt.
After hours of discussion, we finally agreed on a compromise.

finally / after all
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finally
At the end of a process or development, or after a long wait; at last.
Nach stundenlanger Diskussion haben wir uns schließlich auf einen Kompromiss geeinigt.
After hours of discussion, we finally agreed on a compromise.

The word 'schließlich' is derived from 'der Schluss' (the end). This connection to the idea of closure helps you understand the main meaning 'am Ende' (in the end) or 'endlich' (finally).
Wir haben lange diskutiert und schließlich eine Lösung gefunden.
We discussed it for a long time and finally found a solution.
'Schließlich' can be meant temporally ('endlich' = finally) or as a justification ('immerhin' = after all). The temporal meaning concludes a process, while the justifying meaning provides an important reason or context.
Zuerst hat es geregnet, dann geschneit, und schließlich kam die Sonne raus.
First it rained, then it snowed, and finally the sun came out.
When 'schließlich' is at the beginning of a main clause in position 1, the verb follows directly in position 2. This word order is called inversion.
Schließlich verstand er das Problem und konnte es lösen.
Finally, he understood the problem and was able to solve it.
end
'das Ende' and 'schließlich' can both point to the final point in a development. 'Ende' is a noun and names the last part or the conclusion itself. In 'am Ende' (in the end), it can also mean 'ultimately'. 'schließlich' is an adverb and describes that something happens after some time, after several steps, or after waiting. They can be especially easy to confuse because of 'am Ende' and 'schließlich'. As a simple guide: 'das Ende' is the conclusion; 'schließlich' describes that something happens at the end.

Nach drei Anrufen hat mein Bruder schließlich den Termin bekommen.
After three calls, my brother finally got the appointment.
Sie hat am Ende des Gesprächs noch eine wichtige Frage gestellt.
At the end of the conversation, she asked another important question.