If you've run a secure web site, you'll know that it's expensive, inflexible, takes time to set up, and requires you to remember to renew the certificate. Let's Encrypt solves most of those problems for you, at least in a common use case.
If you run a server with a dedicated IP, have privileges to install software on that server (i.e. you can run `apt-get` or `yum`), and you use Apache or Nginx as your HTTP server, then it's brain-dead simple to switch to HTTPS.
Let's Encrypt is planning on going live sometime in the last quarter of 2015. Right now they're in a restricted beta, and users will see browser warnings about your site if you use their certificates. When they go live, they'll be backed by IdenTrust, so users will have the same warning-free experience that any other secure site would have.
But even if it's not ready to use for the general public, you can help them test. (At the moment, you can't use apt or yum to install the Let's Encrypt client. Read these installation instructions instead.)
There are lots of use cases that aren't helped by Let's Encrypt yet. Probably the most glaring are for the legions of us that use $3/month hosting services that don't give us a fixed IP and a way to install the Let's Encrypt client. Still, it's a big step forward for a secure web.