This is the 9422nd most frequent German word.
messne
The word "messne" does not exist in standard German; it may be a misspelling or a dialectal term.
In this sentence, 'messen' is used reflexively ('sich messen') to mean 'to compare oneself' in skill or ability in a competitive sense.
Der Wettbewerb wird zeigen, wer sich besser messen kann.
The competition will show who can measure themselves better.
Here, 'messen' also means 'to measure', specifically referring to determining the length of an object.
Mit dem neuen Lineal kann er die Länge genau messen.
With the new ruler, he can accurately measure the length.
The word 'messen' here is used in its base form meaning 'to measure', referring to the action of determining the duration of time.