"A tincture is a process of soaking plant matter in a solvent. A tincture dissolves the plant material and extracts its beneficial constituents through alcohol, vegetable glycerin, or vinegar. " (https://achs.edu/blog/how-to-make-a-tincture-herbal-medicine/)

Basically, a tincture is a great way to take higher doses of an herb. Also, some chemicals in herbs don't extract well in water, but do in alcohol, so it can contain more of the constituents than you would get out of a tea. Sometimes herbalists use glycerin or vinegar instead of alcohol. This could be for a variety of reasons, including glycerins being more palatable (they are sweet! But don't raise blood sugar), or having the added benefits that vinegar might provide. It also depends on the herbs as to which ones would be better suited to which format.

It's also not always an either or situation, as you could just as easily add a dropper of tincture into a tea if you wanted to! 

Tinctures also travel well, so if you are on the road or in a place where making  a cup of tea just isn't feasible, you might opt for a tincture.