A string of solar panels refers to a number of panels connected together, or "strung," in series. By keeping the strings separate, shading in one area of the system will not affect other strings -- something to which photovoltaic systems are susceptible. Even if there is no obvious shade, snow, dust, and imperfections in the panel can cause problems. Multiple strings can be used to power a single battery, appliance or other load, but their output must be combined into one using a combiner box.
Some inverters actually do the job of the combiner box, and combine the wires coming from the solar panels into a single DC output before converting the current into alternating current (AC), after which it can be connected to lights, motors, or other devices. In this case, a combiner box is not strictly necessary. However, if the inverter does not perform this function, and your system is made of multiple strings, you will need a combiner box to bring your strings together into one DC output.
Perhaps your inverter does the job of the combiner box, making its presence technically redundant. There are still occasions when a combiner box may be desired. One of these is when the inverter or charge controller is far from the array, or when wires must track a difficult course. In these cases, it may be easier to place a combiner box close to the panel. If the system came with a combiner box anyway, you might also save money on wiring.
Even if the inverter does the job of the combiner box, you should install one anyway if your system is particularly large. If your system is grid-connected instead of a stand-alone system, it's possible you have a system that can output more than 600 volts. For systems below 150 volts, a combiner box with a circuit breaker will suffice, but above this, get one that uses fuses -- one for each string is typical -- as most circuit breakers cannot handle more than 150 volts.