
nahezu
almost
Almost, nearly, or approximately. It expresses that a state or quantity has almost been reached.
Nach der langen Wanderung war die Wasserflasche nahezu leer.
After the long hike, the water bottle was almost empty.
almost
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almost
Almost, nearly, or approximately. It expresses that a state or quantity has almost been reached.
Nach der langen Wanderung war die Wasserflasche nahezu leer.
After the long hike, the water bottle was almost empty.
The word is made up of 'nahe' (near) and 'zu' (to). Literally, it expresses that you 'come close' to something or a state, but do not quite reach it.
Wir sind dem Ziel schon sehr nahe.
We are already very close to the goal.
'Nahezu' (almost) belongs more to written language or to an elevated, more formal style. It is used less often in everyday spoken language.
Die Aufgabe war nahezu unmöglich zu lösen.
The task was almost impossible to solve.
'Nahezu' (almost) often comes before adjectives or participles to describe an approximation to a state. Common combinations are 'nahezu unmöglich' (almost impossible), 'nahezu identisch' (almost identical), 'nahezu abgeschlossen' (almost completed), or 'nahezu perfekt' (almost perfect).
Die beiden Bilder sind nahezu identisch.
The two pictures are almost identical.
pretty / fairly
nahezu clearly indicates that a state or quantity has almost been reached. ziemlich can express much the same thing, especially in the phrase so ziemlich, but is otherwise often understood as an indication of degree. For a clear or somewhat formal statement, nahezu is the better choice.

Das ist nahezu alles, was wir für die Reise brauchen.
That is almost everything we need for the trip.
Das ist so ziemlich alles, was wir für die Reise brauchen.
That is pretty much everything we need for the trip.