Analytic philosophy is contrasted with continental philosophy (as in, the European continent), which tends to be more interested in politics, society, the individual, and other less technical topics. An old joke goes like this:
"The analytic philosopher will accuse the continental of being insufficiently clear, while the continental philosopher accuses the analytic of being insufficiently."
Since this is HN, you might be interested in language, logic, and similar topics. If this is the case, you will likely enjoy analytic philosophy, especially Quine, Wittgenstein, Carnap, and Popper.
However, if you are coming at philosophy cold, I really don't recommend the academic analytic path. It's too easy to get lost in the weeds and decide that all this stuff is just too obscure and abstruse to be useful.
If that's the case, I suggest a very brief reading list to shake up your default preconceptions of how the world works. The goal here is to make you question your basic assumptions, which is when philosophy is at its best.
- Meditations by Marcus Aurelius and On the Shortness of Life by Seneca. Classic Stoic works. Very accessible entry points to classical philosophy and Stoicism.
- Beyond Good and Evil by Friedrich Nietzsche. If you read this and understand it, your entire conception of ethics, values, and how we use labels like "good" or "evil" will be shaken up.
- Republic by Plato. If you live in a Western country, you probably think that democracy is the highest and best form of government. Plato thinks otherwise and it's worth understanding why.
- A Tractate on Japanese Aesthetics by Donald Richie. This is a fairly recent book but it serves as an excellent introduction to East Asian and Japanese thought via art and aesthetics.
- I Ching. The Chinese classic is super easy to read and is diametrically opposite to the static, eternal universal Platonic model much of Western thought it built upon.
- You should also probably read something from India, the Islamic world, and Russia, but I wanted to keep my list fairly short. Some recommendations here are The Bhagavad Gita, Ḥayy ibn Yaqẓān, and anything by Dostoyevsky.
For reference: I have a bachelor's in philosophy from a program in the US which is almost exclusively analytic in nature.