Mormons crossing the desert in the 1850s named these Joshua Trees because they created an image of Joshua with his armed raised beckoning them to the Promised Land. Since at best they grow 1/4 in (6 mm) per year, most of these people-sized trees were there hundreds of years earlier.
Joshua Tree National Park is near Palm Springs but much higher and cooler -- most of the Park is around 4500 feet (1370 m). The trees only grow above 3000 feet, and only bloom at this time of the year. Another reason to visit now is because the wildflowers are super in the cooler climate.
The Park is loaded with interesting rock formations -- you can see some little ones here. It attracts many rock climbers because the camping is also nice there.