To work hard for a long time at something difficult.
Slogging can make people feel tired, but also proud of what they have done.
Examples:
I had to slog through all my homework.
She slogged away at her job all day.
We slogged through the deep snow to get home.
He slogged through the muddy field to find the lost ball.
I slogged for hours to finish the puzzle.
They slogged through the hot desert to find water.