Scalable Link Interface (SLI) is a brand name for a multi-GPU solution
developed by NVIDIA for linking two or more video cards together to
produce a single output. SLI is an application of parallel processing
for computer graphics, meant to increase the processing power
available for graphics.
An SLI ready card or power supply means it's capable of adding a second (or more) video card. Adding a second card usually can increase overall performance but there are times when the communication between the two cards can create overhead (see micro stuttering)
You don't specify which video card you currently have but you may not need a second card just to drive three monitors. If you just want to have an extended desktop with three screens your current card may support that option. Depends on the outputs and options. If you want to have three screens for game playing you may need a second card depending on what resolution and level of quality you enable but this is not a requirement. I use a single AMD XFX 6950 on three monitors for both work and gaming just fine.