This is the 14206th most frequent Russian word.
осадками
"Осадками" translates to "precipitation" in English, referring to rain, snow, sleet, etc.
In this sentence, 'осадками' is used in the instrumental case to describe accompanying rain and precipitation.
Завтра ожидаются дожди с осадками.
Rain with precipitation is expected tomorrow.
Here, 'осадков' is in the genitive case to describe precipitation as a source of moisture.
Грунт впитал влагу после осадков.
The soil absorbed moisture after the precipitation.
In this usage, 'осадков' is again in the genitive case, indicating the cause of wetness outside.