Advertisements that are thought to be of interest to you will automatically appear.
Ads that are thought to be aligned with your interests will automatically appear.
「Interest」は「興味」ですね。
「Be of interest to 誰々」は「誰々の興味に合っている」、「誰々の興味を惹く」という意味になります。
「広告」は「advertisement」です。
長いので、よく「ad」に略されます。
Advertisements that are thought to be of interest to you will automatically appear.
あなたの興味を惹くと思われる広告が自動的に出てくる。
Ads that are thought to be aligned with your interests will automatically appear.
あなたの興味に合うと思われる広告が自動的に出てくる。
I found a book that I think will be of interest to you.
あなたの興味を惹くと思われる本を見つけたよ。
Ads that are likely to be of interest to you will automatically appear.
**Ads that are likely to be of interest to you will automatically appear.**
**You’ll automatically see ads that may be of interest to you.**
**“興味を惹く” = be of interest to someone**
これは丁寧で自然な表現で、「〜にとって興味深い」という意味です。