Liddy is to Bathsheba Everdene what Jan Coggan is to Gabriel Oak. Basically, she's a sort of sidekick who's always around when Bathsheba needs to get something off her chest. The book doesn't give her a super complicated personality, but it does tell us that she, "the maltster's great-granddaughter, was about Bathsheba's equal in age, and her face was a prominent advertisement of the light hearted English country-girl" (9.4). In other words, she's a completely normal girl who laughs when things are funny and gasps when things are surprising.
The only other thing we really learn about Liddy is that she's very loyal to Bathsheba and that she's proud to be Bathsheba's right-hand woman. As we read in one of her early descriptions, "Liddy chose a position at [Bathsheba's] elbow, and began to sew, sometimes pausing and looking around, or, with the air of a privileged person" (10.1). She thinks of herself as being distinguished, even though she doesn't have the intelligence or education that Bathsheba does. In the end, though, Bathsheba trusts Liddy enough to make her the maid of honor in her wedding.