When something happens right away, or in an instant, it happens at first sight. Did you fall for your rescue dog the minute you saw her? Then you believe in love at first sight.
You might experience love at first sight in your life — or possibly hatred at first sight. Either way, you're overwhelmed with emotion immediately, the first time you see someone. Another way to use this adverb phrase is to mean "from a first impression." So you might say, "My cat is much meaner than he seems to be at first sight. Be very careful when you pet him."