Gutters are designed to move the water that falls on your roof away from the sides of your house, so that it doesn't pool and damage your foundation. If your gutter is leaking between the edge of the gutter and the side of your house, the solution to your problem will depend on why the water is leaking.
A gutter needs to be sloped toward the downspout so that it drops about a 1.2 cm (1/2 inch) for every 3 m (10 feet) of gutter, and it needs to be consistently sloped throughout the entire gutter run. Without the correct slope, the water will pool in the gutter, and then eventually flow over the side. Place a level near the area where the gutter is leaking to see if the area is sloped. If it is not, you will have to unscrew that section of gutter from the fascia boards and either adjust one side of it higher, or one side of it lower, and then reinstall the gutter into the fascia boards.
Over the years, a large amount of leaves and debris can build-up in the gutter system. Once the leaves start to decompose, they can form watertight mounds that prevent rain from passing them by. When this happens, the water builds up in the gutter until it flows over the sides. To fix this issue, just clean out your gutters with a garden trowel. If your downspouts are blocked, you can remove them and clean them out, or use a plumber's snake to destroy the blockage.
Water leaking between the gutter and the fascia board can also be a result of the gutter not being flush against the side of your house. Check the bolts that connect the gutter to the fascia board to make sure they are screwed all the way in and secure. You can move the gutter bracket up or down the length of gutter if that area of the fascia board is damaged and unable to keep the gutter secure.
At the bottom of your roof there should be a 1.8 cm (3/4 inch) metal ledge that hangs out over the gutter. This drip edge is what directs the water to your gutter, instead of flowing down the side of your house. If your drip edge is missing, or if it is not hanging at least 1.8 cm (3/4 inch) over the side of the house, it can be causing the issue. You can replace the drip edge and secure the new one with roofing cement.
If you notice a small steady stream of water running down between the gutter and the house, instead of a raging torrent, the problem may actually be located somewhere else along the gutter. Most gutter holes happen at the seams between gutter pieces. If the gutter looks to be perfectly installed, but you still see water leaking in an area, pour some food colouring into a bucket of water, then dump the water into your gutter. The coloured water will allow you to see exactly where the gutter is leaking and where you need to repair. Apply a gutter patch to the inside of the gutter where the hole is, or replace the seam piece between two sections of gutter, if that is where the opening is.