"I jump across the river!"
Translation:Átugrom a folyón!
It is some kind of locative(?) I guess. It means "on" or "over" the river. When a boat is moving on/in the river, that is also "folyón". This is a very versatile suffix as we can see.
The "across" is conveyed by "át-", and it needs this suffix on the noun. But you could also use accusative: "Átugrom a folyót" is just as correct.
I jump across the river - átugrom a folyón
I cross the river (by jumping) - átugrom a folyót
This is indefinite conjugation... but ugrik is an "ik" verb, where the én form has -om, -em in the indefinite form.
So that particular form looks just like the definite one.
Usually not a problem because most "ik" verbs are intransitive (can't take an object) and so will never be used in the definite conjugation anyway.
And the ones where it can be ambiguous, well, ambiguity happens. Eszem egy almat (indefinite) / Eszem az almat (definite).