Using filter, you could write something like this:
julia> df = DataFrame(x=rand(10), y=rand((1, 2, NaN), 10).*rand(10))
10×2 DataFrame
Row │ x y
│ Float64 Float64
─────┼──────────────────────
1 │ 0.214967 0.955162
2 │ 0.717033 NaN
3 │ 0.313037 NaN
4 │ 0.925829 0.876826
5 │ 0.77564 0.466991
6 │ 0.524314 0.50265
7 │ 0.564011 NaN
8 │ 0.495634 0.611079
9 │ 0.366369 0.761782
10 │ 0.949455 1.41635
julia> filter(:y => !isnan, df)
7×2 DataFrame
Row │ x y
│ Float64 Float64
─────┼────────────────────
1 │ 0.214967 0.955162
2 │ 0.925829 0.876826
3 │ 0.77564 0.466991
4 │ 0.524314 0.50265
5 │ 0.495634 0.611079
6 │ 0.366369 0.761782
7 │ 0.949455 1.41635
This creates a new DataFrame. If instead you want to delete the rows in the original DataFrame, you can use delete!, for example like so:
julia> delete!(df, isnan.(df.y))
7×2 DataFrame
Row │ x y
│ Float64 Float64
─────┼────────────────────
1 │ 0.214967 0.955162
2 │ 0.925829 0.876826
3 │ 0.77564 0.466991
4 │ 0.524314 0.50265
5 │ 0.495634 0.611079
6 │ 0.366369 0.761782
7 │ 0.949455 1.41635