Per this SE blog post, the "Interesting" list is determined by this algorithm:

Starting with a list of the last 3,000 active questions:

• drop questions containing any of your ignored tags
• drop closed questions if you lack the reputation required to vote for reopening
• drop questions scoring -4 or lower

Next, apply the following score formula to the remaining questions:

your interesting tags +1,500 per interesting tag, up to +2,000 total your top 40 scoring tags max of +1,000 per tag (scaled), up to +2,000 total question score +200 × score, up to +1,000 total total answer score -200 × score, up to -1,000 total number of answers -200 × answers, up to -1,000 total number of views -15 × views, up to -1,000 total question last activity date -1 × (seconds / 15)

Count it all up and take the top 90 by score.

We also mix in a few random questions from the last 3,000 — 10% (9) for logged in users and 20% (18) for anonymous users. We’re like DJs trying to spin a mix of songs — some you might know by heart and love, others you might not have chosen for yourself, but could possibly like if you gave them a fair listen.

That should answer your first two questions about how favorite and ignored tags affect the list, and for your 3rd question, I would assume if a post was tagged with both a favorite and ignored tag, it would get dropped in the very first step.

So the reason it's so good at picking questions you'd be interested in is because it considers the tags to your posts, and the community votes or activity on the post in addition to your favorite and ignored tags.

Per this SE blog post, the "Interesting" list is determined by this algorithm:

Starting with a list of the last 3,000 active questions:

• drop questions containing any of your ignored tags
• drop closed questions if you lack the reputation required to vote for reopening
• drop questions scoring -4 or lower

Next, apply the following score formula to the remaining questions:

your interesting tags +1,500 per interesting tag, up to +2,000 total your top 40 scoring tags max of +1,000 per tag (scaled), up to +2,000 total question score +200 × score, up to +1,000 total total answer score -200 × score, up to -1,000 total number of answers -200 × answers, up to -1,000 total number of views -15 × views, up to -1,000 total question last activity date -1 × (seconds / 15)

Count it all up and take the top 90 by score.

We also mix in a few random questions from the last 3,000 — 10% (9) for logged in users and 20% (18) for anonymous users. We’re like DJs trying to spin a mix of songs — some you might know by heart and love, others you might not have chosen for yourself, but could possibly like if you gave them a fair listen.

That should answer your first two questions about how favorite and ignored tags affect the list, and for your 3rd question, I would assume if a post was tagged with both a favorite and ignored tag, it would get dropped in the very first step.

So the reason it's so good at picking questions you'd be interested in is because it considers the tags to your posts, and the community votes or activity on the post in addition to your favorite and ignored tags.