Why are my gutters allowing water to drip off the fascia and soffit?
Looks like you've got water standing in the gutter. It also looks like you've got a mitered corner on the gutter itself.
Standing water:
Either the gutter is not sloped correctly, or the downspout is clogged.

To check slope, pull off some of those plastic clips and put a long level on the edge of the gutter. If the gutter is dead level, that's your problem - it should slope about 1/4&quot; per foot. If the bubble is off center, that's good. Center the bubble and measure the gap between the level and the top of the gutter - it should be about 1/4&quot; of height for each foot of run.

If it's just debris in the gutter preventing water from flowing to the downspout, or debris in the downspout itself, that's all pretty easy to scoop out. Not fun, necessarily, but an easy fix.


Corner miter:
That miter may not be well sealed. Or, the seal may have failed. Because there's water standing in the gutter, it's slowly dripping through and down the soffit.
You'll have to get the water out of the gutter, then dig into that corner to see what's going on there. You want a good seal between the two pieces of gutter along each wall to ensure the water moves along the gutter to the downspout instead of leaking out at the seam. You may need to clean out the seal the best you can, then squeeze some sealant into the gap.
What's my line?
Additionally, this line at the back of the gutter trough itself just caught my attention. Most gettering I've seen does not have any sort of a bend, break, or other anomaly along the back wall. It might be worth taking a look at this to see what's going on here. If it's a seam of any sort, make sure it's good and tight and sealed.