Check under the table top for any stamps/markings or on the inside of the drawers

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No idea who made it and it would be impossible to tell without a maker's mark...but it's mahogany veneer and possibly some solid mahogany elements, possibly another wood stained mahogany. The style is "traditional"...sort of oa mix of Chippendale, Hepplewhite with a little Jacobean revival thrown in for good measure.
As to what it's worth...only as much as someone would pay....and all that depends on where you are, how quickly you want to sell it and how you are offering it.
Linda c

It's 1920s-40s "Chipplewhite", a blend of various classic styles that was popular at that time. They were either recovering from the massively bulbous legs or the bulbs were coming into style, but you are lucky to have missed the grotesque peak of that fad. The chairs show a trace of it.

When they are well-cared for they are great bits of traditional furniture. They are usually well-built, good scale for a modern house, and you can make up nice stories about Granny who willed it to you.

Value? Depends on your area. And it also depends on your ad-writing ability. I sold a Chipplewhite vanity for $500 when others were unsold at $120 because I described it, identified the era and pointed to ads for similar new pieces for $500 ... that were particleboard.