Unfortunately there is not much you can do until it stops raining.
Once the rain stops, you will need to reseal the top of the meter socket where the cable enters. You can use a good grade of exterior silicon caulk to do this but it must be dry.
I will also advise you to have your meter socket and panel inspected for signs of water damage.
Let me know if you need more information.
Yes it does.
The water is getting past the seal on the top of the meter socket and running down the inside of the cable.
Due to the fact that water has soaked the inside of the panel I highly advise you to have your electrical service inspected. The water can cause mineral deposits on the inside of the breakers that may cause them to not function properly. It can also cause corrosion on the internal connections of the panel that could lead to connectivity issues.
Let me know if you need more help.
Without being able to see the panel I can not tell you that for sure.
I can tell you I have seen this many times over the years. If this is a recent problem it should be fine until you have the problem corrected. Continued exposure to water will eventually lead to the service having to be replaced.