This is the 2779th most frequent Russian word.
наконец
"At last" or "finally."
In this sentence, 'наконец-то' is used to express relief and culmination after waiting or a long process.
Наконец-то я приехал домой после долгой поездки.
Finally, I came home after a long trip.
Here, 'наконец' signifies the completion of the waiting period with the train's arrival.
Мы долго ждали поезд, и он наконец прибыл.
We waited for the train for a long time, and it finally arrived.
The word 'наконец' is used in this context to show the resolution or conclusion of a process of realization.