Hi Christina,
USB 3.0 allows devices to transfer data 10 times as fast as USB 2.0 allows. However, both the port and the device plugged into it need to be USB 3.0 to get the faster speed. If the port is USB 3.0, but the device you plug into it is USB 2.0, then you get USB 2.0 speed. The same is true if you plug a USB 3.0 device into a USB 2.0 port.
However, even if you get a USB 3.0 device and plug it into a USB 3.0 port, you probably won't get the maximum USB 3.0 speed, because (I think) no devices are yet capable of moving reading and writing data that fast, no matter how fast the pipeline (USB 3.0 in this case) allows moving the data through the pipeline. You'll get faster speed than USB 2.0, but not 10 times as fast. That will probably take a few more years, maybe several years. Even today's fastest hard drives, even SSD hard drives, can't read and write data that fast. But they're getting ever faster and faster, and I have no doubt that one day they will be as fast as USB 3.0.
Regarding eSATA:
eSATA is mainly for hard drives. Most USB external hard drives are really PATA or SATA hard drives with circuitry attached to convert the data stream to USB. That conversion makes the data transfer slightly less efficient. eSATA does not require that conversion. So a real-world eSATA drive might have slightly faster real-world data transfer than a USB 3.0 drive.
On the other hand, eSATA drives need to be plugged in separately for power, compared to USB which supplies its own power. And, eSATA cables can't be longer than 6.6 feet (2 meters), while USB cables can be longer.
You might be interested in eSATAp, also known as eSATA/USB. It's a port that provides power over eSATA, but the device must also have an eSATAp plug for it to be able to get power from it and so not need to be plugged in separately. eSATAp is also compatible with USB devices. Each eSATAp port is rated for USB 2.0 or USB 3.0.
So -- you have a USB 2.0 device, and you've been told USB 3.0 is faster. The question is, will that particular device be faster if you connect it to a USB 3.0 port? No. If you plug a USB 2.0 device into a USB 3.0 port, you get USB 2.0 speed. If you want faster performance, you'll need to get a USB 3.0 device and plug it into a USB 3.0 port.
An exception is if you have lots of busy USB devices all daisy-chained and ultimately connected to the same USB connection on the motherboad. All of those devices together are limited by USB 2.0 (or 3.0) bandwidth. If you have so much USB activity going on that your fastest USB device is not getting enough attention, it would be faster if they were all daisy-chained to the same USB 3.0 connection. But it would also be faster if you could give it its own USB 2.0 connection, too. Where your computer has two or more USB ports together, internally they may be daisy-chained into the same motherboard connection.
But that isn't how most people work. Most people have a few low-bandwidth USB devices, like mouse and keyboard, and only one high-bandwidth USB device doing anything important at one time. It would make a difference if you were moving data from a USB flash drive to a USB hard drive.
I hope this helps. Good luck!
Greg