What are the reasons for my 3D prints having large numbers of strings between parts of a layer? I am printing a print using PLA on a Prusa i3 printer and an MK8 extruder, at 210 degrees celsius, 60 mm/sec, sliced with slic3r. The print consists of a base, with 4 tower-like projections that then join with a near-vertical overhang slope that isn't posing a problem for my printer.

However, even before the overhang begins, I am getting large amounts of strings as the extruder head jumps between the four towers in the print, leading to a "spiderweb" effect between them. How can I deal with these strings, and are they a warning that there might be something amiss with my printer, or possible other failures in other parts of the print?
Stringing is often a result of too-high a temperature, or insufficient retraction. When there is highly liquid filament in the nozzle tip, it can adhere to the remainder of the print while dripping as the nozzle moves, leading to a thin string of the filament forming. As further travel moves are performed in each layer, this turns to a web.

The high temperature causes filament to be very liquid, causing it to move downward in the nozzle chamber easily, as opposed to having to be extruded forcefully due to viscosity. The temperature setpoint of 210 was high enough to cause this to happen.

A second possible cause, insufficient retraction, can also be blamed for this issue. Retraction is a process in which the extruder reverses its movement to pull filament back up the hotend, preventing it from dripping at the tip, and forming a string. Most slicers will allow specifying a numeric value in millimeters of filament to be retracted. Remember that printers with Bowden tubes between nozzle/hotend and extruder motor will require increased retraction and priming (extrusion when starting to print after a retract-and-move). Note that too much retraction can cause other problems, such as insufficient plastic in the hotend chamber at the start of the next printing move, which can cause gaps and other issues.