the ARDUINO is a micro-controller.
you program it to do 'stuff'
you can have a sensor that will detect rain drops, really just a circuit board with lots of stripes that would know when water drops hit it.
the Arduino has a rather simple built in timer.
you can use it to water the plants once every 24 hours, for 5 minutes.
both times are things you control.
the output is just as simple low-power output.
to turn on the water valve, you would need to turn on the power to the valve.
google arduino relay to see what we typicaly use.
you can have it set to water the plants each moring around 6:00 AM. and if it rains for some time, it could skip a day.
all under your programming.
to get more information about arduino related things, add arduino to your searches
arduino rain detector
arduino relay
arduino water valve....
arduino sprinkler control.....
this can be a good first project.
I would highly recomend you spend some time with google and then before you buy things, post links to the things here. we can advise if they will work together.