The Sensor Log tab of the PDA has four sub-tabs: Nearby Ships, Stations, Killed List and Killed-By List.
The Nearby Ships tab is by far the most used section of the Sensor Log view. It can be accessed in space by pressing the "u" key. This screen displays all of the ships in the same sector as you are, color-coded by nation. You can sort by Name, Faction, Ship, or Distance by clicking the appropriate column header. Ships within radar range (usually, 5000m) are displayed more brightly than ships outside of radar range. You can also configure your Proximity Warning here. Simply enable the checkbox in the lower-right-hand corner and enter a distance (in meters). Any time another ship comes within that distance of you, your computer will make an audible "beep" to warn you.
Finally, if a ship is within radar range, you can click on it to target it.