Language is definitely the first, especially the more basic components of our languages like numbers or pronouns. There is also religion, food, common behaviors (kind of like the way we interact among ourselves, I’m not sure how to explain it but I can see the similarities), how we greet others, respect for elders and strong family bonds. Nomadic lifestyles are also a common aspect but more for Central Asian turks rather than the ones more in the west like Turkey. They used to follow shamanism before converting to Islam a long time ago. Some turks still practice shamanism today. I also think that depending on geographic location, Turkic people are culturally closer. For example, it seems the northern Siberian turks have more in common with each other while turks more in the west like Turkey and Azerbaijan have more in common. I hope this answered your question! I kept it general because if I went into detail it would be super long lol.
Edit: I would also like to add: Carpets! Turkic people are very into carpets. Our people hand weave and use traditional carpets a lot. Turkic carpets can be distinguished from other cultures’ carpets (like Persian) based on the knots and designs (ours seem to use geometric shapes more).