Agree with the comments that it's assuredly a connection point for a water softener that's since been removed. The top plastic handle provides a bypass for the softener (either when it's broken, or in this case removed). I would anticipate that if you turn the shutoff valve off, you'll turn off water to a significant part of your house, or possibly all of it if this is on the incoming water line to your building. Sometimes there will be a separate cold water feed to the kitchen (so you don't cook/drink with softened water) or to outside faucets, but that's not universal..
If you have plans to install a water softener, then keep it there. If not, then have a qualified person replace that leaky plastic with new permanent copper piping of some sort.