All jumping spiders have excellent eyesight to aid them in hunting. And as their name suggests, they have great jumping abilities, allowing them to leap many times their body length.
However, their most interesting behavior may be how they react to humans. Jumping spiders, when approached by a human, tend to stay put and observe. They can often be handled, and make excellent macro photography subjects if you find an especially tame one.
This "tameness" is unique among spiders and most insects. And the image of being tame and inquisitive is further enhanced by their 'facial features', which appear to impart expressions (see photo below for an example).
Spiders, like many "bugs", consist of thousands of species worldwide. In fact, jumping spiders (family Salticidae) alone contain over 5000 species. When you factor in regional and seasonal variances, it becomes quite a challenge to identify species.
Jumping spiders in general can be loosely identified by the arrangement of their eyes - all in a row, with their middle eyes substantially larger. Behaviorally, they are hunters, so you will not see them with or in a web. They do spin silk to "tether" themselves when jumping.
Habronattus coecatus, public domain image from wikipedia
And be sure to check out my other Macro photos.