You need to install a thresh hold with a seal. like this

That's a grade problem; the ground/pavement is too high, where will the water go?

Thank you for sending the link to a pic of the threshold. Will the rubber part withstand outside weather? I have a threshold like that for an interior door going to the kitchen. Should I dig out the rotted wood and put concrete or ? down before putting the threshold in? Should I use expanding foam or calk under the left part of the frame where there is a gap? Unfortunately I sometimes get water in my basement.

That thresh hold is designed for use on an exterior door.

The floor surface on which the thresh hold is to be installed needs to be flat and as level as possible. With the other problems there are, seems to me a more involved repair is necessary.

Possibly cutting out a section and pouring new concrete, sloping the new away from the house.

As a general rule, trying to stop leaks/water intrusion by using foam/etc. does not last or work well.

Thanks so much for the information. This is very helpful!