Wiring batteries in parallel is an extremely easy way to double, triple, or otherwise increase the capacity of a lithium battery. When wiring lithium batteries in parallel, the capacity (amp hours) and the current carrying capability (amps) are added, while the voltage remains the same.
If your load requires more current than a single battery can provide, but the voltage of the battery is what the load needs, then you need to add batteries in parallel to increase amperage. Wiring batteries in parallel is an extremely easy way to double, triple, or otherwise increase the capacity of a lithium battery.
Consider the example of two batteries connected in parallel: Battery A has a voltage of 6 volts and a current of 2 amps, while Battery B has a voltage of 6 volts and a current of 3 amps. When connected in parallel, the total voltage remains at 6 volts, but the total current increases to 5 amps. Advantages and Disadvantages of Parallel Connections
The batteries are wired in parallel, the load current is split among the batteries in the group. If you have 2 batteries wired in parallel, they will each experience 50% of the total load current. In the same respect, if 5 batteries are wired in parallel, each battery will only experience 20% of the total load current.
If you parallel cells you may have to balance the cells at discharge time either with a small resistance on each or some kind of current mirror circuit (more complex) so they discharge evenly. As the comment mentions, paralleling and short circuiting lithium batteries is potentially very dangerous if you don't know exactly what you are doing.
The parallel-connected batteries are capable of delivering more current than the series-connected batteries but the current actually delivered will depend on the applied voltage and load resistance. You understand Ohm's Law, but the "parallel batteries supply more current" statement should really be "parallel batteries CAN supply more current".