So now that we these partial charges, it begs the question: why does that matter? Well, do you remember the old phrase "opposites attract"? That often is used to describe electricity. Positive attracts negative and vice versa. So now the hydrogen is partially positive, it will be attracted to anything nearby that is negative... or even just partially negative.
So what might be around a water molecule? Well, in a single droplet of water, there are approximately 1.67 x 10^21 molecules of water - that's a lot. Often, there are many other water molecules near one. When they are near on another, they take on a formation similar to that shown here.
The partial negative charges of an oxygen are attracted to the partial positive charges of a nearby molecule's hydrogen atoms, and vice versa. This causes them to form numerous weak bonds between the partially charged atoms. These are known as hydrogen bonds. They are represented by the dashed lines in the image.
They are really weak - nowhere near as strong as a covalent bond. But there are lots of them. I mean LOTS them. Remember how many molecules of water are in just a single drop of water? Now imagine that they're all holding hands.